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A mix of analog sounds produced by handmade electronic circuits and different contact microphones. Its sound architecture leads toward a fuzzy temporal perception although both tracks last the same. mfu034

A mix of analog sounds produced by handmade electronic circuits and different contact microphones. Its sound architecture leads toward a fuzzy temporal perception although both tracks last the same. mfu034

Symmetry - Empty reflections EP

This is a proof of concept for a MIDI device I am working on at ITP (NYU).

One of out first songs

The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the Schwinger-Dunkl algebra sd(2), are investigated. The algebra sd(2) has six generators, including two involutions and a central element, and can be seen as a deformation of the Lie algebra u(2). Two of the symmetry generators, J_3 and J_2, are respectively associated to the separation of variables in Cartesian and polar coordinates. Using the parabosonic creation/annihilation operators, two bases for the representations of sd(2), the Cartesian and circular bases, are constructed. In the Cartesian basis, the operator J_3 is diagonal and the operator J_2 acts in a tridiagonal fashion. In the circular basis, the operator J_2 is block upper-triangular with all blocks 2x2 and the operator J_3 acts in a tridiagonal fashion. The expansion coefficients between the two bases are given by the Krawtchouk polynomials. In the general case, the eigenvectors of J_2 in the circular basis are generated by the Heun polynomials and their components are expressed in terms of the para-Krawtchouk polynomials. In the fully isotropic case, the eigenvectors of J_2 are generated by little -1 Jacobi or ordinary Jacobi polynomials. The basis in which the operator J_2 is diagonal is then considered. In this basis, the defining relations of the Schwinger-Dunkl algebra imply that J_3 acts in a block tridiagonal fashion with all blocks 2x2. The matrix elements of J_3 in this basis are given explicitly.

Finite element modeling of circular ring using half and quarter symmetry

A class of the one-dimensional Schroedinger operators L with the symmetry algebra LB(+/-) = q(+/-2)B(+/-)L, (B(+),B(-)) = P(sub N)(L), is described. Here B(+/-) are the 'q-ladder' operators and P(sub N)(L) is a polynomial of the order N. Peculiarities of the coherent states of this algebra are briefly discussed.

An improved procedure for the three dimensional finite element analysis of an angle ply laminate with a circular hole is discussed. The procecure exploits polar symmetry and is the basis for a new finite element computer code. For the broad class of laminates that contain angle plies, this code requires only one half as much computing capacity as conventional codes.

The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound and Stein's lemma, and derive bounds on these quantities in terms of their corresponding statistical distance measures. A special emphasis is put on the comparison of the performances of group-invariant and unrestricted measurements.

Avramov and Buchweitz proved that for finitely generated modules $M$ and $N$ over a complete intersection local ring $R$, $\Ext^i_R(M,N)=0$ for all $i\gg 0$ implies $\Ext^i_R(N,M)=0$ for all $i\gg 0$. In this note we give some generalizations of this result. Indeed we prove the above mentioned result when (1) $M$ is finitely generated and $N$ is arbitrary, (2) $M$ is arbitrary and $N$ has finite length and (3) $M$ is complete and $N$ is finitely generated.

We predict the generation of noncritically squeezed light through the spontaneous rotational symmetry breaking occurring in a Kerr cavity. The model considers a $\chi^{(3)}$ cavity that is pumped by two Gaussian beams of frequencies $\omega_{1}$ and $\omega_{2}$. The cavity configuration is such that two signal modes of equal frequency $\omega_{\mathrm{s}}=(\omega_{1}% +\omega_{2})/2$ are generated, these signal fields being first order Laguerre--Gauss modes. In this system a spontaneous breaking of the rotational symmetry occurs as the signal field corresponds to a Hermite--Gauss TEM mode. This symmetry breaking leads to the perfect and non--critical (i.e., non dependent on the parameter values) squeezing of the angular momentum of the output TEM mode, which is another TEM mode spatially orthogonal to that in which bright emission occurs.

For any non-degenerate, quasi-homogeneous hypersurface singularity W and an admissible group of diagonal symmetries G, Fan, Jarvis, and Ruan have constructed a cohomological field theory which is a candidate for the mathematical structure behind the Landau-Ginzburg A-model. When using the orbifold Milnor ring of a singularity W as a B-model, and the Frobenius algebra H_{W,G} constructed by Fan, Jarvis, and Ruan, as an A-model, the following conjecture is obtained: For a quasi-homogeneous singularity W and a group G of symmetries of W, there is a dual singularity W^T such that the orbifold A-model of W/G is isomorphic to the B-model of W^T. I will show that this conjecture holds for a two-dimensional invertible loop potential $W$ with its maximal group of diagonal symmetries $G_{W}$.

It is shown how integrability of the generalized Lie equations of continous Moufang transformatiosn is related to the reductivity conditions and Sagle-Yamaguti identity.

Transition from baryonic matter to color-flavor-locked quark matter is described in terms of skyrmion matter changing into half-skyrmion matter. The intermediate phase between the density $n_p$ at which a skyrmion turns into two half skyrmions and the chiral transition density $n_c^{\chi SR}$ at which hadronic matter changes over to quark matter corresponds to a chiral symmetry restored phase characterized by a vanishing quark condensate and a {\em non-vanishing} pion decay constant. When hidden local fields are incorporated, the vector manifestation of Harada-Yamawaki HLS theory implies that as density approaches $n_c^{\chi SR}$, the gauge coupling $g$ goes to zero (in the chiral limit) and the symmetry "swells" to $SU(N_f)^4$ as proposed by Georgi for the "vector limit." This enhanced symmetry, not present in QCD, can be interpreted as "emergent" in medium due to collective excitations. The fractionization of skyrmions into half-skyrmions resembles closely the magnetic N\'eel--to-valence bond solid (VBS) paramagnet transition where "baby" half-skyrmions enter as relevant degrees of freedom in the intermediate phase. It is suggested that the half-skyrmion phase in dense matter corresponds to the "hadronic freedom" regime that plays a singularly important role in inducing kaon condensation that leads to the collapse of massive compact stars into black holes..

The group E_6 for grand unification is combined with the generation symmetry group SO(3)_g. The coupling matrices in the Yukawa interaction are identified with the vacuum expectation values of scalar fields which are representations of the generation symmetry. These values determine the hierarchy of the fermions as well as their mixings and CP-violation. This generation mixing appears in conjunction with the mixing of the standard model fermions with the heavy fermions present in the lowest representation of E_6. A close connection between charged and neutral fermions is observed relating for instance the CKM mixings with the mass splittings of the light neutrinos. Numerical fits with only few parameters reproduce quantitatively all known fermion properties. The model predicts an inverted neutrino hierarchy and gives rather strict values for the light and heavy neutrino masses as well as for the 0\nu 2\beta decay parameter. It also predicts that the masses of the two lightest of six `right handed' neutrinos lie in the low TeV region.

We construct and analyze an ultraviolet extension of a model in which electroweak symmetry breaking is due to both technifermion and top-quark condensates. The model includes dynamical mechanisms for all of the various gauge symmetry breakings. We discuss certain aspects in which it requires additional ingredients to be more realistic.

We demonstrate that the recent paper by Abhinav and Panigrahi entitled `Supersymmetry, PT-symmetry and spectral bifurcation' [Ann.\ Phys.\ 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials having a complex $sl(2)$ potential algebra.

We discuss the recombination of brane/anti-brane pairs carrying $D3$ brane charge in $AdS_5 \times S^5$. These configurations are dual to co-dimension one defects in the ${\cal N}=4$ super-Yang-Mills description. Due to their $D3$ charge, these defects are actually domain walls in the dual gauge theory, interpolating between vacua of different gauge symmetry. A pair of unjoined defects each carry localized $(2+1)$ dimensional fermions and possess a global $U(N)\times U(N)$ flavor symmetry while the recombined brane/anti-brane pairs exhibit only a diagonal U(N). We study the thermodynamics of this flavor-symmetry breaking under the influence of external magnetic field.

In this model, the gravity term in the Lagrangean comes from spontaneous symmetry breaking of an additional scalar quadruplet field $\Upsilon$. The resulting gravitational field is approximate to one of the models of coframe gravity with parameters $\rho_1 + 4 \rho_2 = 0$, $\rho_3 = 0$. This article includes an exact solution of coframe gravity with model parameters $\rho_1 \neq 0$, $\rho_2$ any, $\rho_3 = 0$, which is Newtonian at infinity. An iteration process is given to construct a solution for a given matter-radiation stress-energy tensor.

We study the symmetry properties for solutions of elliptic systems of the type {ll}-\dive(a_1(x,|\nabla u^1|(X))\nabla u^1(X))=F_{1}(x, u^1(X),..., u^n(X)), ... -\dive(a_n(x,|\nabla u^n|(X))\nabla u^n(X))=F_{n}(x, u^1(X),..., u^n(X)), where $x\in \R^m$ with $1\leq m < N$, $X=(x,y)\in \R^m\times \R^{N-m}$, and $F_{1},..., F_{n}$ are the derivatives with respect to $\xi^1,..., \xi^n$ of some $F=F(x,\xi^1,..., \xi^n)$ such that for any $i=1,..., n$ and any fixed $(x,\xi^1,..., \xi^{i-1},\xi^{i+1},..., \xi^n)\in \R^m\times \R^{n-1}$ the map $\xi^i\to F(x,\xi^1,...,\xi^i,..., \xi^n)$ belongs to $C^2(\R)$. We obtain a Poincar\'e-type formula for the solutions of the system and we use it to prove a symmetry result both for stable and for monotone solutions.

We explore the dynamics of spontaneous symmetry breaking in a homogeneous system by thermally quenching an atomic gas with short-range interactions through the Bose-Einstein phase transition. Using homodyne matter-wave interferometry to measure first-order correlation functions, we verify the central quantitative prediction of the Kibble-Zurek theory, namely the homogeneous-system power-law scaling of the coherence length with the quench rate. Moreover, we directly confirm its underlying hypothesis, the freezing of the correlation length near the transition due to critical slowing down. Our measurements agree with beyond mean-field theory, and support the previously unverified expectation that the dynamical critical exponent for this universality class, which includes the $\lambda$-transition of liquid $^4$He, is $z=3/2$.

We describe the fine structure of Dirac states in HgTe/CdHgTe quantum wells of critical and close-to-critical thickness and demonstrate the formation of an anticrossing gap between the tips of the Dirac cones driven by interface inversion asymmetry. By combining symmetry analysis, atomistic calculations, and k-p theory with interface terms, we obtain a quantitative description of the energy spectrum and extract the interface mixing coefficient. The zero-magnetic-field splitting of Dirac cones can be experimentally revealed in studying magnetotransport phenomena, cyclotron resonance, Raman scattering, or THz radiation absorption.

The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. This structure may be related to the existence of a discrete non-Abelian family symmetry. In this paper the family symmetry is the non-Abelian discrete group $\Delta(27)$, a subgroup of $SU(3)$ with triplet and anti-triplet representations. Different frameworks are constructed in which the mixing follows from combining fermion mass terms with the vacuum structure enforced by the discrete symmetry. Mass terms for the fermions originate from familon triplets, anti-triplets or both. Vacuum alignment for the family symmetry breaking familons follows from simple invariants.

We propose a family of {\it local} $\cal{PT}$-symmetric photonic lattices with transverse index gradient $\omega$, where the emergence of {\it stable} Bloch-Zener oscillations are controlled by the degree of non-Hermiticity $\gamma$ of the lattice. In the exact $\cal{PT}$-symmetric phase we identify a condition between $\omega$ and $\gamma$ for which a wavepacket self -imaging together with a cascade of splittings and giant recombinations occurs at various propagation distances. The giant wavepacket recombination is further enhanced by introducing local impurities.

We propose a noncommutative version of the Euclidean Lie algebra $E_2$. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra.

We study square lattice space group symmetry fractionalization in a family of exactly solvable models with $\mathbb{Z}_2$ topological order in two dimensions. In particular, we have obtained a complete understanding of which distinct types of symmetry fractionalization (symmetry classes) can be realized within this class of models, which are generalizations of Kitaev's $\mathbb{Z}_2$ toric code to arbitrary lattices. This question is motivated by earlier work of A. M. Essin and one of us (M. H.), where the idea of symmetry classification was laid out, and which, for square lattice symmetry, produces 2080 symmetry classes consistent with the fusion rules of $\mathbb{Z}_2$ topological order. This approach does not produce a physical model for each symmetry class, and indeed there are reasons to believe that some symmetry classes may not be realizable in strictly two-dimensional systems, thus raising the question of which classes are in fact possible. While our understanding is limited to a restricted class of models, it is complete in the sense that for each of the 2080 possible symmetry classes, we either prove rigorously that the class cannot be realized in our family of models, or we give an explicit model realizing the class. We thus find that exactly 487 symmetry classes are realized in the family of models considered. With a more restrictive type of symmetry action, where space group operations act trivially in the internal Hilbert space of each spin degree of freedom, we find that exactly 82 symmetry classes are realized. In addition, we present a single model that realizes all $2^6 = 64$ types of symmetry fractionalization allowed for a single anyon species ($\mathbb{Z}_2$ charge excitation), as the parameters in the Hamiltonian are varied. The paper concludes with a summary and a discussion of two results pertaining to more general bosonic models.

We describe the Lie group and the group representations associated to the nonlinear Thermodynamic Coordinate Transformations (TCT). The TCT guarantee the validity of the Thermodynamic Covariance Principle (TCP) : {\it The nonlinear closure equations, i.e. the flux-force relations, everywhere and in particular outside the Onsager region, must be covariant under TCT}. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces, i.e. under TCT. The TCP ensures the validity of the fundamental theorems for systems far from equilibrium. The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. We derive the conserved (thermodynamic) currents and, as an example of calculation, a simple system out of equilibrium where the validity of TCP is imposed at the level of the kinetic equations is also analyzed.

We study the parity- and time-reversal PT symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials $\pm i\gamma $ at two end sites. The SSH model is known as one of the simplest two-band topological models which has topologically trivial and nontrivial phases. We find that the non-Hermitian terms can lead to different effects on the properties of the eigenvalues spectrum in topologically trivial and nontrivial phases. In the topologically trivial phase, the system undergos an abrupt transition from unbroken PT-symmetry region to spontaneously broken $\mathcal{PT} $-symmetry region at a certain $\gamma_{c}$, and a second transition occurs at another transition point $\gamma_{c^{'}}$ when further increasing the strength of the imaginary potential $\gamma$. But in the topologically nontrivial phase, the zero-mode edge states become unstable for arbitrary nonzero $\gamma$ and the $\mathcal{PT}$-symmetry of the system is spontaneously broken, which is characterized by the emergence of a pair of conjugated imaginary modes.

We comment on a simple way to accommodate translational symmetry breaking into the recently proposed holographic model which features a superconducting dome-shaped region on the temperature-doping phase diagram.

We present a TeV scale seesaw mechanism for exploring the dark matter and neutrino phenomenology in the light of recent neutrino and cosmology data. A different realization of the Inverse seesaw(ISS) mechanism with $A_{4}$ flavor symmetry is being implemented as a leading contribution to the light neutrino mass matrix which usually gives rise to vanishing reactor mixing angle $\theta_{13}$. Using a non-diagonal form of Dirac neutrino mass matrix and $3\sigma$ values of mass square differences we parameterize the neutrino mass matrix in terms of Dirac Yukawa coupling "$y$". We then use type II seesaw as a perturbation which turns out to be active to have a non-vanishing reactor mixing angle without much disturbing the other neutrino oscillation parameters. Then we constrain a common parameter space satisfying the non-zero $\theta_{13}$, Yukawa coupling and the relic abundance of dark matter. Contributions of neutrinoless double beta decay are also included for standard as well as non-standard interaction. This study may have relevance in future neutrino and Dark Matter experiments.

We investigate the parity of transmission spectra in a photonic crystal (PhC) waveguide with a side-coupled cavity and a partially blocking element. We demonstrate, by means of numerical calculations, that by varying the cavity-block distance the spectra vary from being asymmetric with blue parity, to being symmetric (Lorentzian), to being asymmetric with red parity. For cavity-block distances larger than five PhC lattice constants, we show that the transmission spectrum is accurately described as the transmission spectrum of a Fabry-Perot etalon with a single propagating Bloch mode, and that the parity of the transmission spectrum correlates with the Fabry-Perot roundtrip phase.

We show that suppression of vortices in the Ashkin Teller ferromagnet on a square lattice splits the order-disorder transition and opens up an intermediate phase where the macroscopic symmetry enhances to U(1). When we selectively suppress the formation of non-chiral vortices, chiral vortices proliferate and replace the U(1) phase with a new phase where chiral symmetry is restored. This result demonstrates a fascinating phenomenon in which the symmetry information encoded in topological defects manifests itself in the symmetry of the phase where the defects proliferate. We also show that this phenomenon can occur in all $\mathbb{Z}_n$ ferromagnets with even values of $n$.

We discuss the effective field theory for spacetime symmetry breaking from the local symmetry point of view. By gauging spacetime symmetries, the identification of Nambu-Goldstone (NG) fields and the construction of the effective action are performed based on the breaking pattern of diffeomorphism, local Lorentz, and (an)isotropic Weyl symmetries as well as the internal symmetries including possible central extensions in nonrelativistic systems. Such a local picture distinguishes, e.g., whether the symmetry breaking condensations have spins and provides a correct identification of the physical NG fields, while the standard coset construction based on global symmetry breaking does not. We illustrate that the local picture becomes important in particular when we take into account massive modes associated with symmetry breaking, whose masses are not necessarily high. We also revisit the coset construction for spacetime symmetry breaking. Based on the relation between the Maurer-Cartan one form and connections for spacetime symmetries, we classify the physical meanings of the inverse Higgs constraints by the coordinate dimension of broken symmetries. Inverse Higgs constraints for spacetime symmetries with a higher dimension remove the redundant NG fields, whereas those for dimensionless symmetries can be further classified by the local symmetry breaking pattern.

We model the electrons on a monolayer graphene in terms of the compact and non-compact U(1) lattice gauge theories. The system is analyzed by the strong coupling expansion and is shown to be an insulator due to dynamical gap formation in/around the strong coupling limit. This is similar to the spontaneous chiral symmetry breaking in strong coupling gauge theories. The results from the compact and non-compact formulations are compared up to the next-to-leading order of the strong coupling expansion. Excitonic modes and their dispersion relations in the insulating phase are also investigated: it is found that there arises a pseudo-Nambu--Goldstone mode obeying the Gell-Mann--Oakes--Renner type formula.

The Parity symmetry of the Cosmic Microwave Background (CMB) pattern as seen by WMAP 7 is tested jointly in temperature and polarization at large angular scale. A Quadratic Maximum Likelihood (QML) estimator is applied to the WMAP 7 year low resolution maps to compute all polarized CMB angular power spectra. The analysis is supported by 10000 realistic Monte-Carlo realizations. We confirm the previously reported Parity anomaly for TT in the range $\delta \ell=[2,22]$ at $> 99.5%$ C.L.. No anomalies have been detected in TT for a wider $\ell$ range (up to $\ell_{max}=40$). No violations have been found for EE, TE and BB which we test here for the first time. The cross-spectra TB and EB are found to be consistent with zero. We also forecast {\sc Planck} capabilities in probing Parity violations on low resolution maps.

Working with explicit examples given by the 56 representation in $SU(8)$, and the 10 representation in $SU(5)$, we show that symmetry breaking of a group ${\cal G}\supset {\cal G}_1 \times {\cal G}_2$ by a scalar in a rank three or two antisymmetric tensor representation leads to a number of distinct $modular$ ground states. For these broken symmetry phases, the ground state is periodic in an integer divisor $p$ of $N$, where $N>0$ is the absolute value of the nonzero $U(1)$ generator of the scalar component $\Phi$ that is a singlet under the simple subgroups ${\cal G}_1$ and ${\cal G}_2$. Ground state expectations of fractional powers $\Phi^{p/N}$ provide order parameters that distinguish the different phases. For the case of period $p=1$, this reduces to the usual Higgs mechanism, but for divisors $N\geq p>1$ of $N$ it leads to a modular ground state with periodicity $p$, implementing a discrete Abelian symmetry group $U(1)/Z_p$. This observation may allow new approaches to grand unification and family unification.

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.

We show that there is a special choice of parameters for which the galileon theory is invariant under an enhanced shift symmetry whose non-linear part is quadratic in the coordinates. This symmetry fixes the theory to be equivalent to one with only even powers of the field, with no free coefficients, and accounts for the improved soft limit behavior observed in the quartic galileon S-matrix.

We demonstrate fully demixed (separated) robust and stable bright binary dipolar Bose-Einstein condensate soliton in a quasi-one-dimensional setting formed due to dipolar interactions for repulsive contact interactions. For large repulsive interspecies contact interaction the first species may spatially separate from the second species thus forming a demixed configuration, which can be spatially-symmetric or symmetry-broken. In the spatially-symmetric case, one of the the species occupies the central region, whereas the other species separates into two equal parts and stay predominantly out of this central region. In the symmetry-broken case, the two species stay side by side. Stability phase diagrams for the binary solitons are obtained. The results are illustrated with realistic values of parameters in the binary 164Dy-168Er and 164Dy-162Dy mixtures. The demixed solitons are really soliton molecules formed of two types of atoms. A proposal for creating dipolar solitons in experiments is also presented.

One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking.

Dual conformal symmetry has had a huge impact on our understanding of planar scattering amplitudes in N=4 super Yang-Mills. At tree level, it combines with the original conformal symmetry generators to a Yangian algebra, a hallmark of integrability, and helps in determining the tree-level amplitudes. The latter are now known in closed form. At loop level, it determines the functional form of the four- and five-point scattering amplitudes to all orders in the coupling constant, and gives restrictions at six points and beyond. The symmetry is best understood at loop level in terms of a novel AdS-inspired infrared regularization which makes the symmetry exact, despite the infrared divergences. This has important consequences for the basis of loop integrals in this theory. Recently, a number of selective reviews have appeared which discuss dual conformal symmetry, mostly at tree level. Here, we give an up-to-date account of dual conformal symmetry, focussing on its status at loop level.

We start with the relation between the chiral symmetry breaking and gauge field topology. New lattice result further enhance the notion of Zero Mode Zone, a very narrow strip of states with quasizero Dirac eigenvalues. Then we move to the issue of "origin of mass" and Brown-RHo scaling: a number of empirical facts contradicts to the idea that masses of quarks and such hadrons as $\rho,N$ decrease near $T_c$. We argue that while at $T=0$ the main contribution to the effective quark mass is chirally odd $m_{\snchi}$, near $T_c$ it rotates to chirally-even component $m_\chi$, because "infinite clusters" of topological solitons gets split into finite ones. Recent progress in understanding of topology require introduction of nonzero holonomy $\neq 0$, which splits instantons into $N_c$ (anti)selfdual "instanton-dyons". Qualitative progress, as well as first numerical studios of the dyon ensemble are reported. New connections between chiral symmetry breaking and confinement are recently understood, since instanton-dyons generates holonomy potential with a minimum at confining value, if the ensemble is dense enough.

Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial, and algebraic properties. They can be viewed as finite or infinite 3-periodic graphs (nets) equipped with additional structure imposed by the faces, allowed to be skew, zig-zag, or helical. A polyhedron or complex is "regular" if its geometric symmetry group is transitive on the flags (incident vertex-edge-face triples). There are 48 regular polyhedra (18 finite polyhedra and 30 infinite apeirohedra), as well as 25 regular polygonal complexes, all infinite, which are not polyhedra. Their edge graphs are nets well-known to crystallographers, and we identify them explicitly. There also are 6 infinite families of "chiral" apeirohedra, which have two orbits on the flags such that adjacent flags lie in different orbits.

It has been found in numerical experiments that when one removes a sector from an elastic sheet and glues the edges of the sector back together, the resulting configuration is radially symmetric and nearly conical. We make a rigorous analysis of this setting under two simplyfying assumptions: Firstly, we only consider radially symmetric configurations. Secondly, we consider the so-called von-K\'arm\'an limit, where the size of the removed region as well as the deformations are small. We choose free boundary conditions for a sheet of infinite size. We show existence of minimizers of the suitably renormalized free energy functional. As a by-product, we obtain a lower bound for the elastic energy that has been conjectured in the related context of d-cones. Moreover, we determine the shape of minimizers at infinity up to exponentially decaying terms.

A variational technique is established to deal with the Schrodinger equation with parity-time(PT) symmetric Gaussian complex potential. The method is extended to the linear and self-focusing and defocusing nonlinear cases. Some unusual properties in PT systems such as transverse power flow and PT breaking points can be analyzed by this method. Following numerical simulations, the analytical results are in good agreement with the numerical results.

The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular by the appearance of bound states. A recently developed quantum statistical (QS) approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.

In quantum spin liquids, fractional spinon excitations carry half-integer spins and other fractional quantum numbers of lattice and time-reversal symmetries. Different patterns of symmetry fractionalization distinguish different spin liquid phases. In this work, we derive a general constraint on the symmetry fractionalization of spinons in a gapped spin liquid, realized in a system with an odd number of spin-$1/2$ per unit cell. In particular, when applied to kagome/triangular lattices, we obtain a complete classification of symmetric gapped $\mathbb{Z_2}$ spin liquids.

Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c-axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.

1Letters of a Woman Homesteader

By Elinore Pruitt Stewart

The writer of the following letters is a young woman who lost her husband in a railroad accident and went to Denver to seek support for herself and her two-year-old daughter, Jerrine. Turning her hand to the nearest work, she went out by the day as house-cleaner and laundress. Later, seeking to better herself, she accepted employment as a housekeeper for a well-to-do Scotch cattle-man, Mr. Stewart, who had taken up a quarter-section in Wyoming. The letters, written through several years to a former employer in Denver, tell the story of her new life in the new country. They are genuine letters, and are printed as written, except for occasional omissions and the alteration of some of the names. (Publishers’ Note, May 1914)

2Perfect Behavior

By Donald Ogden Stewart

A humorous guide to manners and etiquette for ladies and gentlemen in a social "crises," published in 1922. (Introduction by Samanem)

Maria W. Stewart was America's first black woman political writer. Between 1831 and 1833, she gave four speeches on the topics of slavery and women's rights. <em>Meditations From The Pen of Mrs. Maria W. Stewart</em>—published in 1879, shortly before her death—is a collection of those speeches as well as her memoir, some meditations and prayers. They are political, poetical and sermon all at the same time; but in the milieu in which she lectured, they were a critically important part of the abolitionist movement years before the contributions of others such as Frederick Douglass and Sojourner Truth. Her speeches and essays espoused a return to Christian values and morality, but also proposed fundamental changes in gender roles in the midst of tremendous public opposition to the rights of blacks and of women. (Introduction by James K. White)

4Uncle Josh's Punkin Centre Stories

By Cal Stewart

A collection of comedic short stories from the perspective of an old country man. (Summary by Philip Martin)

5Letters on an Elk Hunt

By Elinore Pruitt Stewart

This is a sequel to Letters of a Woman Homesteader in which Elinore Rupert (Pruitt) Stewart describes her arrival and early years on a Burntfork Wyoming ranch in 1909-1913. The letters are written to her elderly friend, Mrs. Coney, in Denver. In the present collection of letters, Elinore describes a lively excursion on horseback and wagon into the Wyoming wilderness during July-October 1914. Her traveling companions are her husband “Mr. Stewart,” their three oldest children, and kind-hearted, opinionated neighbor Mrs. O’Shaughnessy. Mr. Haynes (organizer of the hunt) and his friend, Mr. Struble (the cheerful big man of the party) lead the group, and are also joined by physician Dr. Teschall, “a moving-picture man” Mr. Harkrudder, Professor Glenholdt seeking “the tip-end bone of the tail of a brontosaurus” and his students (“two geological fellows” who “talk of nothing but strata and formation”). Also joining the group is Mr. Murry with his tiresome accordion.<br><br>Although some hunting is accomplished on the trip, the overarching focus of Elinore’s letters is on descriptions of awe-inspiring Wyoming scenery and the interesting people she encounters. With her familiar wit and wisdom, Elinore also writes of tragedies and romances she observes during her trip -- that is, whenever Elinore’s effort to observe is not thwarted by “the good mon” Mr. Stewart. In one letter Elinore complains to Mrs. Coney that “Mr. Stewart is the queerest man: instead of letting me enjoy the tableau [the reunion of two long-lost lovers], he solemnly drove on, saying he would not want any one gawking at him if he were the happy man. Anyway, he couldn’t urge Chub [the horse] fast enough to prevent my seeing and hearing what I’ve told you.”<br><br>By the time the adventurers are homeward bound with their supply of elk meat, Elinore is homesick for her youngest child, Junior, at home with his grandmother; Mrs. O’Shaughnessy has taken in two young orphans; and quiet, young Mr. Haynes complains good-naturedly about having to travel along with a rolling nursery.<br><br>Elinore’s letters capture an interesting transition point in history. People traveled by horse and wagon, there were cowboys and cattle stampedes, and medical care was rustic. At the same time, automobiles and modern medicine, archeology and motion picture making were entering the scene and war was commencing in Europe. (Note to more sensitive readers: Elk hunting is described in Chapters 7 and 8.) (Summary by Lynne Carroll)

6Perfect Behavior (Version 2)

By Donald Ogden Stewart

A humorous guide for ladies and gentlemen in all social crises. (Summary by MaryAnn)

7Parody Outline of History

By Donald Ogden Stewart

" Mr. H. G. Wells, in his "Outline of History," was of necessity forced to omit the narration of many of the chief events in the history of these United States. Such omissions I have in this brief volume endeavored to supply. And as American history can possibly best be written by Americans and as we have among us no H. G. Wells, I have imagined an American history as written conjointly by a group of our most characteristic literary figures." - Summary by Donald Ogden Stewart

Welcome back to another exciting collection courtesy of the little known but influential pulp magazine The Thrill Book! In this issue we continue the mystical Egyptian mystery "The Jeweled Ibis" and the daring jungle adventure "In the Shadows of Race" as well as bringing a new full-length raucous and rowdy western "A Hooting, Tooting Son-of-a-Gun" as well as a quality selection of additional stories, poems and other assorted articles. - Summary by Ben Tucker

9Case With Nine Solutions

By Alfred Walter Stewart

This book was written by Alfred Walter Stewart under the pseudonym J.J. Connington: Sir Clinton Driffield is a respected police professional assigned the task of solving a convoluted crime of murder. The case involves a coy temptress, her husband, a secret admirer and a young man with a romantic interest in the temptress. Sir Clinton and his assistant, Inspector Flamborough must whittle down the circumstances and causes of death from nine potential scenarios. The process leads them through scientific clues, messages from a secret source and good old fashioned deductive reasoning. - Summary by Howard Skyman

10Murder In The Maze

By Alfred Walter Stewart

This is another story written by Walter Stewart under the pseudonym of J.J. Connington. His character of Sir Clinton Driffield, the chief constable, is challenged with solving crimes committed in the maze of the Shandon family estate. The Shandons are a successful if flawed set of brothers but all is not well beneath the surface of the privileged lives of their extended family. Jealousies and ambitions cause trouble as they often do. Sir Clinton and his faithful associate Wendover endeavour to unravel a mystery as complex as the maze itself. - Summary by Howard Skyman

11Dangerfield Talisman

By Alfred Walter Stewart

The Dangerfield family resides on an estate steeped in history and tradition. At the centre of this is a much coveted and admired piece of jewelry called the Dangerfield Talisman. A group of guests gathers at the estate for a mixture of business and pleasure. The pleasure provides entertainment for the idle rich while the business is that of a foreigner attempting to purchase the famed article. During their visit the talisman disappears for not the first time in its history and the hunt begins to expose the thief. What this endeavour also exposes are sub-plots involving the different characters in the story and the various dramas and difficulties they encounter. - Summary by Howard Skyman