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In this paper we show a density property for fractional weighted Sobolev spaces. That is, we prove that any function in a fractional weighted Sobolev space can be approximated by a smooth function with compact support. The additional difficulty in this nonlocal setting is caused by the fact that the weights are not necessarily translation invariant.

We study a non-homogeneous boundary value problem in a smooth bounded domain in $\mathbb{R}^N$. We prove the existence of at least two nonnegative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma.

We discuss some recent results by Parini and Ruf on a Moser-Trudinger type inequality in the setting of Sobolev-Slobodeckij spaces in dimension one. We push further their analysis considering the inequality on the whole $\mathbb{R}$ and we give an answer to one of their open questions.

In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration--Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico.

In this article, we re-examine some of the classical pointwise multiplication theorems in Sobolev-Slobodeckij spaces, and along the way we cite a simple counter-example that illustrates how certain multiplication theorems fail in Sobolev-Slobodeckij spaces when a bounded domain is replaced by Rn. We identify the source of the failure, and examine why the same failure is not encountered in Bessel potential spaces. To analyze the situation carefully, we begin with a survey of the classical multiplication results stated and proved in the 1977 article of Zolesio, and we carefully distinguish between the case of spaces defined on the all of Rn and spaces defined on a bounded domain (with e.g. a Lipschitz boundary). However, the survey we give has a few new wrinkles; the proofs we include are based almost exclusively on interpolation theory rather than Littlewood-Paley theory and Besov spaces, and some of the results we give and their proofs, including the results for negative exponents, do not appear in the literature in the way presented here. We also include a particularly important variation of one of the multiplication theorems that is relevant to the study of nonlinear PDE systems arising in general relativity and other areas. The conditions for multiplication to be continuous in the case of Sobolev-Slobodeckij spaces are somewhat subtle and intertwined, and as a result, the multiplication theorems of Zolesio in 1977 have been cited (more than once) in the standard literature in slightly more generality than what is actually proved by Zolesio, and in cases that allow for the construction of counter-examples such as the one included here.

We consider the most general class of linear boundary-value problems for higher-order ordinary differential systems whose solutions and right-hand sides belong to the corresponding Sobolev spaces. For parameter-dependent problems from this class, we obtain a constructive criterion under which their solutions are continuous in the Sobolev space with respect to the parameter. We also obtain a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem. These results are applied to a new broad class of parameter-dependent multipoint boundary-value problems.

We consider the subcritical SQG equation in its natural scale invariant Sobolev space and prove the existence of a global attractor of optimal regularity. The proof is based on a new energy estimate in Sobolev spaces to bootstrap the regularity to the optimal level, derived by means of nonlinear lower bounds on the fractional laplacian. This estimate appears to be new in the literature, and allows a sharp use of the subcritical nature of the $L^\infty$ bounds for this problem. As a byproduct, we obtain attractors for weak solutions as well. Moreover, we study the critical limit of the attractors and prove their stability and upper-semicontinuity with respect to the strength of the diffusion.

Given a finite dimensional manifold $N$, the group $\operatorname{Diff}_{\mathcal S}(N)$ of diffeomorphism of $N$ which fall suitably rapidly to the identity, acts on the manifold $B(M,N)$ of submanifolds on $N$ of diffeomorphism type $M$ where $M$ is a compact manifold with $\dim M

Let $b_{\alpha}^{p}(\mathbb{R}^{1+n}_{+})$ be the space of solutions to the parabolic equation $\partial_{t}u+(-\triangle)^{\alpha}u=0$ $(\alpha\in(0, 1])$ having finite $L^{p}(\mathbb{R}^{1+n}_{+})$ norm. We characterize nonnegative Radon measures $\mu$ on $\mathbb{R}^{1+n}_{+}$ having the property $\|u\|_{L^{q}(\mathbb{R}^{1+n}_{+},\mu)}\lesssim \|u\|_{\dot{W}^{1,p}(\mathbb{R}^{1+n}_{+})},$ $1\leq p\leq q

The affine synthesis operator is shown to map the mixed-norm sequence space $\ell^1(\ell^p)$ surjectively onto $L^p(\Rd), 1 \leq p < \infty$, assuming the Fourier transform of the synthesizer does not vanish at the origin and the synthesizer has some decay near infinity. Hence the standard norm on $f \in L^p(\Rd)$ is equivalent to the minimal coefficient norm of realizations of $f$ in terms of the affine system. We further show the synthesis operator maps a discrete Hardy space onto $H^1(\Rd)$, which yields a norm equivalence for Hardy space involving convolution with a discrete Riesz kernel sequence. Coefficient norm equivalences are established also for Sobolev spaces, by applying difference operators to the coefficient sequences.

Let $K$ be a compact subset of $\bar{\bold C} ={\bold R}^2$ and let $K^c$ denote its complement. We say $K\in HR$, $K$ is holomorphically removable, if whenever $F:\bar{\bold C} \to\bar{\bold C}$ is a homeomorphism and $F$ is holomorphic off $K$, then $F$ is a M\"obius transformation. By composing with a M\"obius transform, we may assume $F(\infty )=\infty$. The contribution of this paper is to show that a large class of sets are $HR$. Our motivation for these results is that these sets occur naturally (e.g. as certain Julia sets) in dynamical systems, and the property of being $HR$ plays an important role in the Douady-Hubbard description of their structure.

The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in H^s({\mathbb{R}), -3/10

We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation \[ -\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq \mathbb{R}^{N},\ N\geq 3, \] where $\Omega $ is a radial domain (bounded or unbounded) and $u$ satisfies $u=0$ on $\partial \Omega $ if $\Omega \neq \mathbb{R}^{N}$ and $u\rightarrow 0$ as $\left| x\right| \rightarrow \infty $ if $\Omega $ is unbounded. The potential $V$ may be vanishing or unbounded at zero or at infinity and the nonlinearity $g$ may be superlinear or sublinear. If $g$ is sublinear, the case with $g\left( \left| \cdot \right| ,0\right) \neq 0$ is also considered.

In this work we estend a recent result of Krist\'aly, Marzantowicz and Varga concerning the existence of three critical points certain non-smooth functionals. Using this result, we guarantee the existence of three solutions to a inclusion quasilinear problem, with non-homogeneous boundary condition through Orlicz Sobolev spaces.

We study dispersive mixed-order systems of pseudodifferential operators in the setting of $L^p$-Sobolev spaces. Under the weak condition of quasi-hyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of $L^p$-Sobolev spaces, a strongly continuous semigroup is in many cases only generated if $p=2$ or $n=1$. The results are applied to the linear thermoelastic plate equation inertial term and with Fourier's or Maxwell-Cattaneo's law of heat conduction.

We consider Sobolev spaces with values in Banach spaces as they are frequently useful in applied problems. Given two Banach spaces $X\neq\{0\}$ and $Y$, each Lipschitz continuous mapping $F:X\rightarrow Y$ gives rise to a mapping $u\mapsto F\circ u$ from $W^{1,p}(\Omega,X)$ to $W^{1,p}(\Omega,Y)$ if and only if $Y$ has the Radon-Nikodym Property. But if $F$ is one-sided Gateaux differentiable no condition on the space is needed. We also study when weak properties in the sense of duality imply strong properties. Our results are applied to prove embedding theorems, a multi-dimensional version of the Aubin-Lions Lemma and characterizations of the space $W^{1,p}_0(\Omega,X)$.

We prove a characterization of some $L^p$-Sobolev spaces involving the quadratic symmetrization of the Calder\'on commutator kernel, which is related to a square function with differences of difference quotients. An endpoint weak type estimate is established for functions in homogeneous Hardy-Sobolev spaces $\dot H^1_\alpha$. We also use a local version of this square function to characterize pointwise differentiability for functions in the Zygmund class.

We study the interpolation property of Sobolev spaces of order 1 denoted by $W^{1}_{p,V}$, arising from Schr\"{o}dinger operators with positive potential. We show that for $1\leq p_1 s_0$, $W^{1}_{p,V}$ is a real interpolation space between $W_{p_1,V}^{1}$ and $W_{p_2,V}^{1}$ on some classes of manifolds and Lie groups. The constants $s_{0}, q_{0}$ depend on our hypotheses.

We consider uniformly elliptic and parabolic second-order equations with bounded zeroth-order and bounded VMO leading coefficients and possibly growing first-order coefficients. We look for solutions which are summable to the $p$-th power with respect to the usual Lebesgue measure along with their first and second-order derivatives with respect to the spatial variable.

We derive sharp Sobolev inequalities for Sobolev spaces on metric spaces. In particular, we obtain new sharp Sobolev embeddings and Faber-Krahn estimates for H\"{o}rmander vector fields.

Given bounded domains $\Omega_1$ and $\Omega_2$ in $\mathds{R}^N$ and an isometry $T$ from $W^{1,p}(\Omega_1)$ to $W^{1,p}(\Omega_2)$, we give sufficient conditions ensuring that $T$ corresponds to a rigid motion of the space, i.e., $Tu = \pm (u \circ \xi)$ for an isometry $\xi$, and that the domains are congruent. More general versions of the involved results are obtained along the way.

ICTP Postgraduate Diploma Course in Mathematics - Lectures on Partial Differential Equations -- NOTE: This course was recorded automatically in slots of one hour and processed without human intervention. Lectures are split between videos; their starting time may not coincide with the beginning of videos and intervals were not removed.

The Riemann Mapping Theorem states existence of a conformal homeomorphism $\varphi$ of a simply connected plane domain $\Omega\subset\mathbb C$ with non-empty boundary onto the unit disc $\mathbb D\subset \mathbb C$. In the first part of the paper we study embeddings of Sobolev spaces $\overset{\circ}{W_{p}^{1}}(\Omega)$ into weighted Lebesgue spaces $L_{q}(\Omega,h)$ with an {}"universal" weight that is Jacobian of $\varphi$ i.e. $h(z):=J(z,\varphi)=| \varphi'(z)|^2$. Weighted Lebesgue spaces with such weights depend only on a conformal structure of $\Omega$. By this reason we call the weights $h(z)$ conformal weights. In the second part of the paper we prove compactness of embeddings of Sobolev spaces $\overset{\circ}{W_{2}^{1}}(\Omega)$ into $L_{q}(\Omega,h)$ for any $1\leq q

(Revised version, January 2006. S. Gouezel pointed out that, when 1

In this paper, the authors characterize Sobolev spaces $W^{\alpha,p}({\mathbb R}^n)$ with the smoothness order $\alpha\in(0,2]$ and $p\in(\max\{1, \frac{2n}{2\alpha+n}\},\infty)$, via the Lusin area function and the Littlewood-Paley $g_\lambda^\ast$-function in terms of centered ball averages. The authors also show that the condition $p\in(\max\{1, \frac{2n}{2\alpha+n}\},\infty)$ is nearly sharp in the sense that these characterizations are no longer true when $p\in (1,\max\{1, \frac{2n}{2\alpha+n}\})$. These characterizations provide a new possible way to introduce fractional Sobolev spaces with smoothness order in $(1,2]$ on metric measure spaces.

We consider the well-posedness of the initial value problem associated to the k-generalized Zakharov-Kuznetsov equation in fractional weighted Sobolev spaces. Our method of proof is based on the contraction mapping principle and it mainly relies on the well-posedness results recently obtained for this equation in the Sobolev spaces H^s(\R^2) and a new pointwise commutator type formula involving the group induced by the linear part of the equation and the fractional anisotropic weights to be considered

We give a Sobolev inequality characterisation for the vanishing of a fundamental class in the controlled coarse homology of Nowak and Spakula for quasiconvex uniform spaces that support a local weak $(1,1)$-Poincar\'e inequality. As applications, we consider visual Gromov hyperbolic spaces and Carnot groups.

Let $\sigma\in(0,1)$ with $\sigma\neq\frac{1}{2}$. We investigate the fractional nonlinear Schr\"odinger equation in $\mathbb R^d$: $$i\partial_tu+(-\Delta)^\sigma u+\mu|u|^{p-1}u=0,\, u(0)=u_0\in H^s,$$ where $(-\Delta)^\sigma$ is the Fourier multiplier of symbol $|\xi|^{2\sigma}$, and $\mu=\pm 1$. This model has been introduced by Laskin in quantum physics \cite{laskin}. We establish local well-posedness and ill-posedness in Sobolev spaces for power-type nonlinearities.

For $\beta>0$ and $p\ge 1$, the generalized Ces\`aro operator $$ \mathcal{C}_\beta f(t):=\frac{\beta}{t^\beta}\int_0^t (t-s)^{\beta-1}f(s)ds $$ and its companion operator $\mathcal{C}_\beta^*$ defined on Sobolev spaces $\mathcal{T}_p^{(\alpha)}(t^\alpha)$ and $\mathcal{T}_p^{(\alpha)}(| t|^\alpha)$ (where $\alpha\ge 0$ is the fractional order of derivation and are embedded in $L^p(\RR^+)$ and $L^p(\RR)$ respectively) are studied. We prove that if $p>1$, then $\mathcal{C}_\beta$ and $\mathcal{C}_\beta^*$ are bounded operators and commute on $\mathcal{T}_p^{(\alpha)}(t^\alpha)$ and $\mathcal{T}_p^{(\alpha)}(| t|^\alpha)$. We show explicitly the spectra $\sigma (\mathcal{C}_\beta)$ and $\sigma (\mathcal{C}_\beta^*)$ and its operator norms (which depend on $p$). For $1 < p\le 2$, we prove that $ \hat{{\mathcal C}_\beta(f)}={\mathcal C}_\beta^*(\hat{f})$ and $\hat{{\mathcal C}_\beta^*(f)}={\mathcal C}_\beta(\hat{f})$ where $\hat{f}$ is the Fourier transform of a function $f\in L^p(\RR)$.

In this work we consider the initial value problem (IVP) associated to the two dimensional Zakharov-Kuznetsov equation $$\left. \begin{array}{rl} u_t+\partial_x^3 u+\partial_x \partial_y^2 u +u \partial_x u &\hspace{-2mm}=0,\qquad\qquad (x,y)\in\mathbb R^2,\; t\in\mathbb R,\\ u(x,y,0)&\hspace{-2mm}=u_0(x,y). \end{array} \right\}$$ We study the well-posedness of the IVP in the weighted Sobolev spaces $$H^s(\mathbb R^2) \cap L^2((1+x^2+y^2)^{r} dx dy),$$ with $s,r\in\mathbb R$.

Newtonian spaces generalize first-order Sobolev spaces to abstract metric measure spaces. In this paper, we study regularity of Newtonian functions based on quasi-Banach function lattices. Their (weak) quasi-continuity is established, assuming density of continuous functions. The corresponding Sobolev capacity is shown to be an outer capacity. Assuming sufficiently high integrability of upper gradients, Newtonian functions are shown to be (essentially) bounded and (H\"older) continuous. Particular focus is put on the borderline case when the degree of integrability equals the "dimension of the measure". If Lipschitz functions are dense in a Newtonian space on a proper metric space, then locally Lipschitz functions are proven dense in the corresponding Newtonian space on open subsets, where no hypotheses (besides being open) are put on these sets.

The wave-Sobolev spaces $H^{s,b}$ are $L^2$-based Sobolev spaces on the Minkowski space-time $\R^{1+n}$, with Fourier weights are adapted to the symbol of the d'Alembertian. They are a standard tool in the study of regularity properties of nonlinear wave equations, and in such applications the need arises for product estimates in these spaces. Unfortunately, it seems that with every new application some estimates come up which have not yet appeared in the literature, and then one has to resort to a set of well-established procedures for proving the missing estimates. To relieve the tedium of having to constantly fill in such gaps "by hand", we make here a systematic effort to determine the complete set of estimates in the bilinear case. We determine a set of necessary conditions for a product estimate $H^{s_1,b_1} \cdot H^{s_2,b_2} \hookrightarrow H^{-s_0,-b_0}$ to hold. These conditions define a polyhedron $\Omega$ in the space $\R^6$ of exponents $(s_0,s_1,s_2,b_0,b_1,b_2)$. We then show, in space dimension $n=3$, that all points in the interior of $\Omega$, and all points on the faces minus the edges, give product estimates. We can also allow some but not all points on the edges, but here we do not claim to have the sharp result. The corresponding result for $n=2$ and $n=1$ will be published elsewhere.

This paper extends characterizations of Sobolev spaces by Bourgain, Br\'{e}zis, and Mironescu to the higher order case. As a byproduct, we obtain an integral condition for the Taylor remainder term, which implies that the function is a polynomial. Similar questions are also considered in the context of Whitney jets.

This paper extends characterizations of Sobolev spaces by Bourgain, Br\'{e}zis, and Mironescu to the higher order case. As a byproduct, we obtain an integral condition for the Taylor remainder term, which implies that the function is a polynomial. Similar questions are also considered in the context of Whitney jets.

In this paper, we characterize parabolic Besov and parabolic Sobolev spaces in ${\bf R}^{n+1}$ and ${\bf R}^{n+1}_T, \,\, T > 0$. We also, study the relation between parabolic Besov spaces in ${\bf R}^{n}_T, \,\, T > 0$ and standard Besov space in $\R$.

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces $H^s(\Omega)$ and $\widetilde{H}^s(\Omega)$, for $s\in \mathbb{R}$ and an open $\Omega\subset \mathbb{R}^n$. We exhibit examples in one and two dimensions of sets $\Omega$ for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if $\Omega$ is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

We consider the problem of finding the optimal exponent in the Moser-Trudinger inequality \[ \sup \left\{\int_\Omega \exp{\left(\alpha\,|u|^{\frac{N}{N-s}}\right)}\,\bigg|\,u \in \widetilde{W}^{s,p}_0(\Omega),\,[u]_{W^{s,p}(\mathbb{R}^N)}\leq 1 \right\} < + \infty.\] Here $\Omega$ is a bounded domain of $\mathbb{R}^N$ ($N\geq 2$), $s \in (0,1)$, $sp = N$, $\widetilde{W}^{s,p}_0(\Omega)$ is a Sobolev-Slobodeckij space, and $[\cdot]_{W^{s,p}(\mathbb{R}^N)}$ is the associated Gagliardo seminorm. We exhibit an explicit exponent $\alpha^*_{s,N}>0$, which does not depend on $\Omega$, such that the Moser-Trudinger inequality does not hold true for $\alpha \in (\alpha^*_{s,N},+\infty)$.

We study the well-posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl type equations that are derived from the incompressible MHD system with non-slip boundary condition on the velocity and perfectly conducting condition on the magnetic field. Under the assumption that the initial tangential magnetic field is not zero, we establish the local-in-time existence, uniqueness of solution for the nonlinear MHD boundary layer equations. Compared with the well-posedness theory of the classical Prandtl equations for which the monotonicity condition of the tangential velocity plays a crucial role, this monotonicity condition is not needed for MHD boundary layer. This justifies the physical understanding that the magnetic field has a stabilizing effect on MHD boundary layer in rigorous mathematics.

We prove that the initial value problem associated to a perturbation of the Benjamin-Ono equation or Chen-Lee equation $u_t+uu_x+\beta \mathcal{H}u_{xx}+\eta (\mathcal{H}u_x - u_{xx})=0$, where $x\in \mathbb{T}$, $t> 0$, $\eta >0$ and $\mathcal{H}$ denotes the usual Hilbert transform, is locally and globally well-posed in the Sobolev spaces $H^s(\mathbb{T})$ for any $s>-\frac{1}{2}$. We also prove some ill-posedness issues when $s

In this note we establish the boundedness properties of local maximal operators $M_G$ on the fractional Sobolev spaces $W^{s,p}(G)$ whenever $G$ is an open set in $\mathbb{R}^n$, $0

In \cite{JB1}, Benameur proved a blow-up result of the non regular solution of $(NSE)$ in the Sobolev-Gevrey spaces. In this paper we improve this result, precisely we give an exponential type explosion in Sobolev-Gevrey spaces with less regularity on the initial condition. Fourier analysis is used.

We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible Navier-Stokes equations and the Boltzmann equation. In particular, the optimal decay rates of the higher-order spatial derivatives of solutions are obtained. The negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis.

Given two measurable functions $V(r)\geq 0$ and $K(r)> 0$, $r>0$, we define the weighted spaces \[ H_V^1 = \{u \in D^{1,2}(\mathbb{R}^N): \int_{\mathbb{R}^N}V(|x|)u^{2}dx < \infty \}, \quad L_K^q = L^q(\mathbb{R}^N,K(|x|)dx) \] and study the compact embeddings of the radial subspace of $H_V^1$ into $L_K^{q_1}+L_K^{q_2}$, and thus into $L_K^q$ ($=L_K^q+L_K^q$) as a particular case. Both super- and sub-quadratic exponents $q_1$, $q_2$ and $q$ are considered. Our results do not require any compatibility between how the potentials $V$ and $K$ behave at the origin and at infinity, and essentially rely on power type estimates of their relative growth, not of the potentials separately. Applications to existence results for nonlinear elliptic problems like \[ -\triangle u + V(|x|)u = f(|x|,u) \quad \text{in}\mathbb{R}^N, \quad u \in H_V^1, \] will be given in a forthcoming paper.

We study {\Gamma}-convergence of nonconvex variational integrals of the calculus of variations in the setting of Cheeger-Sobolev spaces. Applications to relaxation and homogenization are given.

We study relaxation of nonconvex integrals of the calculus of variations in the setting of Cheeger-Sobolev spaces when the integrand has not polynomial growth and can take infinite values.

We study relaxation of nonconvex integrals of the calculus of variations in the setting of Cheeger-Sobolev spaces when the integrand has not polynomial growth and can take infinite values.

The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from $\RR^n$. The analysis interestingly combines use of Poincar\'e inequalities and of some Hardy type inequalities.

The aim of this work is to study the first order Dirac-Sobolev spaces in $L^p$ norm on an open subset of ${\mathbb R}^3$ to clarify its relationship with the corresponding Sobolev spaces. It is shown that for $1 < p

The main purpose of our paper is to prove sharp Adams-type inequalities in unbounded domains of $\mathbb{R}^{n}$ for the Sobolev space $W^{m,\frac{n}{m}}\left(\mathbb{R} ^{n}\right)$ for any positive integer $m$ less than $n$. Our results complement those of Ruf and Sani \cite{RS} where such inequalities are only established for even integer $m$. Our inequalities are also a generalization of the Adams-type inequalities in the special case $n=2m=4$ proved in \cite{Y} and stronger than those in \cite{RS} when $n=2m$ for all positive integer $m$ by using different Sobolev norms.

For $1

1Theory of Social Revolutions

By Brooks Adams

Brooks Adams (1848-1927), was an American historian and a critic of capitalism. He believed that commercial civilizations rise and fall in predictable cycles. First, masses of people draw together in large population centers and engage in commercial activities. As their desire for wealth grows, they discard spiritual and creative values. Their greed leads to distrust and dishonesty, and eventually the society crumbles. In The Law of Civilisation and Decay (1895), Adams noted that as new population centers emerged in the west, centers of world trade shifted from Constantinople to Venice to Amsterdam to London. He predicted in America’s Economic Supremacy (1900) that New York would become the centre for world trade. The Theory of Social Revolutions was written in 1913. (Wikipedia)

2Cattle Brands

By Andy Adams

Cattle Brands is a collection of 14 entertaining short stories depicting not only the life of cowboys in the wild, wild West, but also the harrowing skirmishes with banditos, thrilling shoot-outs, attempt at and the recapture of stolen chattel from fierce desperados, and much, much more exciting accounts that make one think it all actually happened. (Summary by Kehinde)

3Log of a Cowboy

By Andy Adams

The Log of a Cowboy is an account of a five-month drive of 3,000 cattle from Brownsville, Texas, to Montana in 1882 along the Great Western Cattle Trail. Although the book is fiction, it is firmly based on Adams's own experiences on the trail, and it is considered by many to be the best account of cowboy life in literature. Adams was disgusted by the unrealistic cowboy fiction being published in his day; The Log of a Cowboy was his response. It is still in print, and even modern reviewers consider it a compelling classic. The Chicago Herald said: "As a narrative of cowboy life, Andy Adams' book is clearly the real thing. It carries its own certificate of authentic first-hand experience on every page." (Introduction by Wikipedia)

4Education of Henry Adams

By Henry Brooks Adams

The Education of Henry Adams records the struggle of Bostonian Henry Adams (1838-1918), in early old age, to come to terms with the dawning 20th century, so different from the world of his youth. It is also a sharp critique of 19th century educational theory and practice. In 1907, Adams began privately circulating copies of a limited edition printed at his own expense. Commercial publication had to await its author's 1918 death, whereupon it won the 1919 Pulitzer Prize. (Introduction by Wikipedia)

5Making a Rock Garden

By Henry Sherman Adams

A short look at building a rock garden, right from the rocks themselves and how to arrange them, to choosing and placing the plants, touching wall and bog gardens, too. In this little monograph, the author is trying to draw the eyes of U.S. gardeners in to the intimate beauty of this neglected hobby.<br><br> (The original work has a number of attractive and useful photographs and drawings.)

6Outlet

By Andy Adams

Andy Adams worked as a cowboy on trail drives from Texas for eight years. This is an account of a drive when he was the foreman of a herd of Texas cattle being driven to Montana. Expect the same quality writing as found in other books by Adams. (Summary by Richard Kilmer)

Abigail Adams lived the American Revolution as the wife of one of its central figures--John Adams. Her family correspondence, published along with a memoir by her grandson, Charles Francis Adams, brings that era into eloquent focus. What was it like to hear the cannon's roar from your window? to face pestilence? food shortages? rampant inflation? devalued coinage? to raise four children alone--and earn the money to keep your household afloat, while your husband was engaged in politics and diplomacy miles and oceans away . . . for years at a time? It's all there in her private letters, letters that were never meant for public eyes, letters that she repeatedly asked to be burned!<br /><br /> Writing to her husband, Abigail expressed anguish at nearby fighting: June 18, 1775, "Charlestown is laid in ashes . . . How many have fallen we know not. The constant roar of the cannon is so distressing, that we cannot eat, drink, or sleep." Yet, she displayed constant fortitude: August 5, 1777, "It is almost thirteen years since we were united, but not more than half that time have we had the happiness of living together. The unfeeling world may consider it in what light they please. I consider it as a sacrifice to my country . . ." And she enlivened her writing with pithy accounts of Revolutionary doings: July 31, 1777, "You must know that there is a great scarcity of sugar and coffee . . . An eminent, wealthy, stingy merchant had a hogshead of coffee in his store, which he refused to sell . . . under six shillings per pound. A number of females . . . assembled with a cart and trucks, marched down to the warehouse, and demanded the keys, which he refused to deliver. Upon which, one of them seized him by his neck . . ." The women "then opened the warehouse, hoisted out the coffee themselves, put it into the truck and drove off. . . .A large concourse of men stood amazed, silent spectators of the whole transaction."<br /><br /> Abigail’s letters, letters of "a vigorous mind," are a fascinating read. (Introduction by Sue Anderson)

8Democracy - An American Novel

By Henry Brooks Adams

Not until after his death in 1918 was it revealed that Henry Adams was the anonymous author of Democracy, which had been published to great acclaim in 1880. Though the book avoids dates and the characters are fictitious, the setting is no doubt that of Washington in the 1870s, the age of Presidents Grant and Hayes. The young widow, Madeleine Lee, wealthy and independent, is the protagonist, who leaves her New York for Washington to turn her intelligence to politics and to see what makes her country tick. There she meets (among others) Senator Silas P. Ratcliffe of Illinois, one of the most powerful and influential (if somewhat uncultured) men of the capital, who is considering a run for the presidency, and who needs a wife to act as First Lady, a position that (he thinks) Mrs. Lee would admirably fill. Through the book Adams plays with the themes of political necessity, compromise, corruption -- particularly the kind of corporate domination of national politics that he saw becoming all too powerful. Should honest and intelligent men keep their integrity by avoiding politics? Or would that simply mean turning over the governance of the country to power-hungry, scheming, and none too honest hacks? For all the witty conversations in his novel, this was a theme that plagued Adams (a presidential grandson) in life as well as literature, and it is a theme that has by no means disappeared today. (Introduction by Nicholas Clifford)</p>

9Secret of Lonesome Cove

By Samuel Hopkins Adams

A body is found on the beach not far from a New England town one morning. Curiously, nobody recognizes the dead woman, and nobody in or near the town seems to be a suspect in a possible murder, therefore most of them assume that she simply washed ashore from a passing vessel. Only problem is vessels didn't pass that stretch of the coast because of it's peculiar tides and eddies; hence its name, Lonesome Cove. Following the finding of the body, the officials of the town start acting a bit peculiar towards how to handle the dead body. The sheriff, the attorney in the town, the village gossip, and even the town doctor all seem to want the identification of the body hushed up. And therefore the body is immediately buried, and the officials hope all will be forgotten and done with. Cause of death: drowning. Enter Chester Kent, who isn't convinced in the same way that the townspeople are, and is willing to pull at his ear lobe in an effort to determine the identity of the body, and how it came to it's demise. (Introduction by Roger Melin)

10Reed Anthony, Cowman: An Autobiography

By Andy Adams

Adams breathes life into the story of a Texas cowboy who becomes a wealthy and influential cattleman.. (Introduction by Wikipedia)

11Wanted: A Husband

By Samuel Hopkins Adams

This serious, yet witty and hilarious, romantic comedy by Samuel Hopkins Adams is a must read/listen! From the very beginning it intrigues you with the troubles and feminine woes of young Miss Darcy Cole. Being a dowdy, unkempt fledgling lady, she finds herself in a mirthful fix after telling a whopper to her room-mates in order to save face from her severely lacking personal life. Resentful and jealous of most all other women, and contemplating suicide, she turns to actress Gloria Greene for guidance on how to become more attractive. Miss Cole had no idea what she was getting herself into! Was it even possible to make herself over? How on Earth would she get through the lie of being engaged to a “titled” man, no less! She had never even met Sir Montrose Veyze, let alone be engaged to him! And then there is the charming Jack Remsen, who seems to be in a pickle himself. Darcy knows he would never fall for someone like her; in fact, no man even looks at her! But perhaps he might be coerced into unwittingly helping her out of her predicament.<br /><br /> A true Ugly Duckling tale, Darcy experiences all the emotions that most ALL women have felt at one time or another throughout life. As quoted by the Proof Listener for this work, the narrator does a superb job of “capturing the spirit of the book!” Drawing the listener in and allowing the audience to live and feel the experience along with the characters. A highly entertaining and riveting book! (summary by reader)

12Notting Hill Mystery

By Charles Warren Adams

Charles Felix was the pseudonym of Charles Warren Adams, an English Lawyer and publisher and is now known to have been the author of "The Notting Hill Mystery", thought to be the first full length detective novel in English.<br /><br /> The story first appeared as an eight part serial in a weekly magazine in 1862, and was subsequently published as a single volume novel in 1865.</p> The story deals with the then newly emerging field of 'mesmerism' which we now know as hypnotism, and its use in the planning and execution of three truly devious crimes. The novel, unusually, is written wholly in the form of a series of letters and reports gathered by the investigator from the various witnesses in the case, and the reader is left to decide themselves the guilt or otherwise of the chief suspect. (summary by Kevin Green)

This is a small volume of poems by Canadian women's rights activist and educator Mary Adams. - Summary by Carolin

14State of the Union Addresses by United States Presidents (1790 - 1816)

By John Adams, Thomas Jefferson, James Madison and George Washington

The State of the Union address is a speech presented by the President of the United States to a joint session of the United States Congress, typically delivered annually. The address not only reports on the condition of the nation but also allows the President to outline his legislative agenda (for which he needs the cooperation of Congress) and national priorities. This album contains recordings of addresses from Washington, Adams, Jefferson, and Madison. - Summary by Wikipedia and Linette Geisel

15State of the Union Addresses by United States Presidents (1817 - 1828)

By John Quincy Adams and James Monroe

The State of the Union address is a speech presented by the President of the United States to a joint session of the United States Congress, typically delivered annually. The address not only reports on the condition of the nation but also allows the President to outline his legislative agenda (for which he needs the cooperation of Congress) and national priorities. This album contains recordings of addresses from James Monroe and John Quincy Adams. (Wikipedia and Linette Geisel)

Arguably one of America's greatest writers, Washington Irving is the author of such classics as "Legend of Sleepy Hollow," "Bracebridge Hall," and "Knickerbocker's History of New York." This book is a concise and extremely entertaining biography of this unique author. <br> Note to the listener: There are a couple of typos in this text. Chapter 33 should have been numbered as chapter 32, and there are two chapter 35's. The readers have keep the typos in the reading, therefore, there is no chapter 32, and the two chapter 35's are designated at "the first" and "the second." - Summary by Greg Giordano

17One Among So Many

By Francis William Lauderdale Adams

Adams' energy and drive can be seen through his large output of written work in his short lifetime. He often wrote quickly and did little revision, living as he did on the proceeds of his own work rather than with the support of a family or sinecure. Songs of the Army of the Night has been reprinted in many editions, but the reputation of these poems ascends from their engagement with social issues, rather than their value as pure poetry for Adams was deeply sympathetic towards downtrodden races and men. - Summary by Wikipedia

18Mystery of the Chinese Ring

By Andy Adams

The Mystery of the Chinese Ring is an exotic adventure story and is set in locations such as Burma and China, with the historical and political ramifications which applied to the mid Twentieth Century and still ring true in the early 21st Century. What is the purpose of the ring? What is the significance of the letter “K”? Why the interest in a sixteen year old boy going to visit a relative in Burma? Why are family dynasties so important, and why the secrecy concerning their survival? This is an audiobook that will find eager listeners from the ages of about ten to octogenarians, male and female, and also those enjoying adventure stories with many twists and turns. The author, Andy Adams, was a well known writer of cowboy books which are thought to be the best in that genre, and his Biff Brewster books, of which he wrote three, are likewise highly regarded. As the main hero is aged sixteen, this story will find resonances in all those that are young in heart, and is an entertaining book in its own right. - Summary by Peter thomlinson

19Brazilian Gold Mine Mystery

By Andy Adams

Mystery adventure, fiction ( Peter Thomlinson). This is a very exciting and gripping story set in the jungles of Brazil and Venezuela, and the quest for the famous El Dorado gold. Incidents with dangerous wild animals, not to mention encounters with head hunters and other native tribes, plus some black magic hocus-pocus all add to the suspense. Double dealing and threats as well as actual confrontations all make life difficult for our brave heroes, and often cause the expedition problems which slows down the quest for the yellow gold. This is a good geography lesson also, and readers will learn about all those huge rivers that flow through these regions, including the huge River Amazon.

20Hawaiian Sea Hunt Mystery

By Andy Adams

Adventure series in exotic locations. This adventure is set in the exotic Island of Hawaii and involves the search for a missing sloop and the whereabouts of a valuable mine. Biff Brewster, his father and friends become entangled with ruthless criminals who are also intending to find the sunken boat and discover the map and the mine. They have kidnapped the elderly scientist who holds the key to the discovery. An exciting adventure with lots of action on land and sea.- Summary by Peter Thomlinson

21Nothing of Importance

By John Bernard Pye Adams

Fighting in France during the Great War, Bernard Adams, an officer with a Welsh battalion, was moved to chronicle what he saw and experienced: the living conditions and duties of officers and “Tommies” (enlisted men) in their dank, rat-infested trenches and behind the lines; the maiming and deaths; and the quiet periods described in official reports as “nothing of importance”. Adams relates his wounding in June, 1916 and its aftermath. The concluding chapter, which he wrote during his convalescence in “Blighty” (soldiers’ slang for England), is an impassioned reflection on war. Following several months of recuperation Adams returned to the front where, on February 26, 1917 he was wounded again. The following day he died. (Lee Smalley)

22Texas Matchmaker

By Andy Adams

As a boy Andy Adams helped with the cattle and horses on the family farm. During the early 1880s he went to Texas, where he stayed for 10 years, spending much of that time driving cattle on the western trails. A Texas Matchmaker is a narrative that describes the work of a cowboy on a large southTexas ranch during the late 1800’s. Adams is considered to be one of foremost writers of the life of the real American cowboy. (Summary by Richard Kilmer)

23Chant of the Firemen

By Francis William Lauderdale Adams

Francis William Lauderdale Adams was an essayist, poet, dramatist, novelist and journalist who produced a large volume of work in his short life. A self-professed 'Child of his Age', Adams combined in his life and work many distinctive features of both fin de siècle British culture and the Australian radical nationalism of the 1890s, including a strong sympathy with socialist and feminist movements. - Summary by Wikipedia

24Celebrated Women Travellers of the Nineteenth Century

By W. H. Davenport Adams

The nineteenth century saw the expansion in popularity of travel among the wealthy. Add to this the independence more women were enjoying as they were released from work in the home, and we have the recipe for some intrepid female travelers. Here we see the stories of just some such adventurous women. - Summary by Lynne Thompson

25Mystery of the Ambush in India

By Andy Adams

Another Biff Brewster adventure story set this time in exotic and mystical India with much of the action around and near the Himalayas. This story brings together all of the friends that Biff Brewster has made in his previous adventures plus a couple of new friends, and involves his father and Uncle Charles once again, and the other members of his family. Some of the events are spectacular, and tension is held by the involvement of an international spy and other situations including riots in Calcutta, poisonous snakes, a mad tiger, and wild bears, as well as a strange religious cult.

26Women I'm Not Married To

By Franklin Pierce Adams

This poem, by Franklin P. Adams, is the sequel to/answer to Dorothy Parker's poem, Women I'm Not Married To, with a decidedly different but equally humorous take on the matter. ( Summary by Michele Fry )

The Premier has decided that being married would be good for his image. He asks his stenographer for advice: (Premier) Good. Just jot me down a precis of the points made by your fifteen admirers when proposing - the points that specially appealed to you. (Stenographer) I'm afraid, sir, that what most appealed to me could not be expressed in words. In fact, it wasn't words. But no, sir. The subject is too sacred.... (Premier)...But you could tell me how they began. The opening address, eh? How did they lead up? (Stenographer) Most of 'em just kissed me, sir. It seemed to give them confidence. (Premier) But I couldn't possibly start like that. (Stenographer) It's always done sir.... - Summary by ToddHW <BR><BR>Cast list:<BR> Herbert Dix, The Premier's Chief Private Secretary: <a href="https://librivox.org/reader/12916">Peter Musgrove</a><br> Effie Bimm, Stenographer in the Premier's Room: <a href="https://librivox.org/reader/11084">Devorah Allen</a><br> Gregory, Chief Messenger at Parliament House: <a href="https://librivox.org/reader/7170">alanmapstone</a><br> William Power, Premier: <a href="https://librivox.org/reader/8879">Son of the Exiles</a><br> Patrick O'Reilly, A Constituent: <a href="https://librivox.org/reader/11790">TJ Burns</a><br> Edward Vyce, The Party Whip: <a href="https://librivox.org/reader/10614">Leanne Yau</a><br> Martha Callender, The Premier's Sister: <a href="https://librivox.org/reader/6281">Beth Thomas</a><br> Charles Lukin, Reporter on The Tribune: <a href="https://librivox.org/reader/10789">Tomas Peter</a><br> Helen Pretty, A widow, the owner of Wyonora Estate: <a href="https://librivox.org/reader/10179">Sonia</a><br> Mrs. Cusack, A friend of Mrs. Pretty's: <a href="https://librivox.org/reader/10087">Sandra Schmit</a><br> Vernon Harrington, Leader of the Opposition: <a href="https://librivox.org/reader/12948">MajorToast</a><br> Maid: <a href="https://librivox.org/reader/10614">Leanne Yau</a><br> Stage Directions and Editing by: <a href="https://librivox.org/reader/6754">ToddHW</a>

28Perils in the Transvaal and Zululand

By Henry Cadwallader Adams

A young man travels to South Africa to find his Mother and sister. He wants to be a clergyman and a farmer when he arrives there. This story includes accounts of the Zulu-Boer wars. - Summary by Ingrid Kennedy

Here we have a serious family drama by Australian playwright Arthur Adams about legacy and responsibilities, with some question about exactly who exactly the Wasters in society are. "No; you produce nothing, you spend everything; you do nothing, you waste everything. You're parasites, useless parasites.... Parasites, inefficients, wasters, wasters!" "We may be parasites, but you have made us parasites. We may be wasters, but you prey on us." To highlight the growing tensions, it includes comic second act scenes placed in the women's undergarment department of the family store. - Summary by ToddHW <BR><BR>Cast list:<BR> John Dangar: <a href="https://librivox.org/reader/13022">Josh Kibbey</a><br> Baby Dangar: <a href="https://librivox.org/reader/10614">Leanne Yau</a><br> Guy Dangar: <a href="https://librivox.org/reader/13072">Campbell Schelp</a><br> Butler: <a href="https://librivox.org/reader/6754">ToddHW</a><br> Anthony Clibborn: <a href="https://librivox.org/reader/12874">Aaron White</a><br> Lindsay Thong: <a href="https://librivox.org/reader/10789">Tomas Peter</a><br> Tossie Quork: <a href="https://librivox.org/reader/11084">Devorah Allen</a><br> J. Charteris Maggs: <a href="https://librivox.org/reader/8879">Son of the Exiles</a><br> Mrs. Goodsir: <a href="https://librivox.org/reader/9743">Ulrike Denis</a><br> Mrs. Megget: <a href="https://librivox.org/reader/13127">Betsy Walker</a><br> Mrs. Cronk: <a href="https://librivox.org/reader/11790">TJ Burns</a><br> Elizabeth Hebblethwaite: <a href="https://librivox.org/reader/12500">Foon</a><br> Mrs. Clibborn: <a href="https://librivox.org/reader/12823">Pauline Latournerie</a><br> Stage Directions: <a href="https://librivox.org/reader/10179">Sonia</a><br> Edited by: <a href="https://librivox.org/reader/6754">ToddHW</a>

30Nequa or The Problem of the Ages

By Jack Adams

<i>Nequa or The Problem of the Ages</i> is one of the first feminist science fiction books published in the United States. It was first serialized in the newspaper Equity, and two editions were published in Topeka, Kansas in 1900. The voyage described in Nequa is to the Arctic. The captain of the ship is amazed to find that when they reach a certain spot, which should be close to the North Pole, the compass shows that the ship is suddenly traveling south. Actually they have sailed into the interior of the earth, where they meet the Altrurians, a people who have developed into a more cooperative society than those of the outer earth. Individual Altrurians describe how the evolution of their society took place. These explanations reflect the Populist thought of the time, with definite feminist proclivities, thereby providing the tone of a political novel. <br>While the book was published with the pseudonym of Jack Adams, it was copyrighted under the names Alcanoan A. Grigsby and Mary P. Lowe, who are presumed to be the true authors. - Summary by Jeff Burke