Downloads & Free Reading Options - Results

Wind tunnel investigation of laminar, transitional, and turbulent boundary layer profiles on wedge at hypersonic speed to confirm theoretical analysis

This discussion focuses upon potential implications of research conducted on preservice teachers' understanding of introductory topics from elementary number theory. Comments interlace three levels of consideration and recapitulate what is striking as some of the most interesting and important findings raised in the presentations, and flesh out some of the theoretical presuppositions underlying these findings. The potential of these findings with respect to practical classroom applications is also discussed. Finally, consideration is given as to why these kinds of phenomena are observed, what may be responsible for their emergence, and what might be done differently in elementary mathematics teacher education. (Contains 14 references.) (Author/ASK)

This discussion focuses upon potential implications of research conducted on preservice teachers' understanding of introductory topics from elementary number theory. Comments interlace three levels of consideration and recapitulate what is striking as some of the most interesting and important findings raised in the presentations, and flesh out some of the theoretical presuppositions underlying these findings. The potential of these findings with respect to practical classroom applications is also discussed. Finally, consideration is given as to why these kinds of phenomena are observed, what may be responsible for their emergence, and what might be done differently in elementary mathematics teacher education. (Contains 14 references.) (Author/ASK)

The spin-charge-family theory, in which spinors carry besides the Dirac spin also the second kind of the Clifford object, no charges, is a kind of the Kaluza-Klein theories. The Dirac spinors of one Weyl representation in $d=(13+1)$ manifest in $d=(3+1)$ at low energies all the properties of quarks and leptons assumed by the standard model. The second kind of spins explains the origin of families. Spinors interact with the vielbeins and the two kinds of the spin connection fields, the gauge fields of the two kinds of the Clifford objects, which manifest in $d=(3+1)$ besides the gravity and the known gauge vector fields also several scalar gauge fields. Scalars with the space index $s\in (7,8)$ carry the weak charge and the hyper charge ($\mp \frac{1}{2}, \pm \frac{1}{2}$, respectively), explaining the origin of the Higgs and the Yukawa couplings. It is demonstrated in this paper that the scalar fields with the space index $t\in (9,10,\dots,14)$ carry the triplet colour charges, causing transitions of antileptons and antiquarks into quarks and back, enabling the appearance and the decay of baryons. These scalar fields are offering in the presence of the right handed neutrino condensate, which breaks the ${\cal C}{\cal P}$ symmetry, the answer to the question about the matter-antimatter asymmetry.

The author surveys the problem of piecing together integral or rational solutions to Diophantine equations (global structure) from solutions modulo congruences and real solutions (local structure).

fasuso jevukutapi xusul pafekelo

In the framework of the Density Functional Theory for superconductors, we study the restoration of the particle number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed. Both are related to the fact that neither the many-body Hamiltonian nor the wave function of the system appear explicitly in the Density Functional Theory. Similar obstacles are encountered in self-consistent theories utilizing density-dependent effective interactions.

In the framework of the Density Functional Theory for superconductors, we study the restoration of the particle number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed. Both are related to the fact that neither the many-body Hamiltonian nor the wave function of the system appear explicitly in the Density Functional Theory. Similar obstacles are encountered in self-consistent theories utilizing density-dependent effective interactions.

We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing lengths and with different closure properties. We give examples of natural number systems incomparable in length; we define hierarchies of natural number systems closed under increasingly powerful functions; and we describe a method by which to construct natural number systems with given closure properties. These natural number systems form natural models for various systems of weak arithmetic.

We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing lengths and with different closure properties. We give examples of natural number systems incomparable in length; we define hierarchies of natural number systems closed under increasingly powerful functions; and we describe a method by which to construct natural number systems with given closure properties. These natural number systems form natural models for various systems of weak arithmetic.

Set out here are some fundamental theories that may be regarded as newly discovered metamathematics of the odd integers in relation to the Collatz conjecture (also called the 3x+1 problem). Originally motivated by the requirement to invent a new optimised integer factorisation method, this foundational paper primarily focuses on the foundation, formalisation and presentation of a new theoretical framework (schema or blueprint) of a Collatz based number system. The proposed framework is based on metamathematical theories meticulously derived through iterative analyses and reverse engineering (i.e., by hand and mathematical computations) of many large subsets of integers. A collation of the fundamental results from these analytical attempts has led to the establishment of a completely deterministic model of a generalised Collatz based number system that is fundamentally and strangely associated with nonchaotic patterns. The proposed Collatz based number schema comprises of both visual and theoretical representations of many hidden patterns in Collatz sequences yet to be reported in literature. This novel theoretical approach may be viewed as a new method to contemporary Collatz conjecture research which may be connected to the proofs of many other mathematical theorems in number theory and discrete mathematics.

Set out here are some fundamental theories that may be regarded as newly discovered metamathematics of the odd integers in relation to the Collatz conjecture (also called the 3x+1 problem). Originally motivated by the requirement to invent a new optimised integer factorisation method, this foundational paper primarily focuses on the foundation, formalisation and presentation of a new theoretical framework (schema or blueprint) of a Collatz based number system. The proposed framework is based on metamathematical theories meticulously derived through iterative analyses and reverse engineering (i.e., by hand and mathematical computations) of many large subsets of integers. A collation of the fundamental results from these analytical attempts has led to the establishment of a completely deterministic model of a generalised Collatz based number system that is fundamentally and strangely associated with nonchaotic patterns. The proposed Collatz based number schema comprises of both visual and theoretical representations of many hidden patterns in Collatz sequences yet to be reported in literature. This novel theoretical approach may be viewed as a new method to contemporary Collatz conjecture research which may be connected to the proofs of many other mathematical theorems in number theory and discrete mathematics.

We introduce a powerful connection between Ehrhart theory and additive number theory, and use it to produce infinitely many new classes of inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope. This greatly improves upon the three known classes of inequalities, which were proved using techniques from commutative algebra and combinatorics. As an application, we deduce all possible `balanced' inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope containing an interior lattice point, in dimension at most 6.

In this note we study numerically the combinatorics of curves and geodesics on the torus with one boundary component. A potential computational difficulty is avoided by counting inside specific orbits of the mapping class group up to a certain length, either geometric or combinatorial. Some cases are rigurolosly determined and the Euler totient function emerges. More complicated orbits are computed to suggest an array of formulae continuing to involve the Euler totient function. We formulate six precise conjectures. These include a novel study of an "inverse" function of the Mirzakhani's asymptotics. The geometric part of our study was motivated by the rationality aspect of these asymptotics.

The Kaluza-Klein compactification in the limit of large number of extra dimensions is studied. Starting point is the Einstein-Hilbert action plus cosmological constant in 4+D dimensions. It is shown that in the large D limit the effective four dimensional cosmological constant is of order 1/D whereas the size of the extra dimensions remains finite. A 't Hooft like large D expansion of the effective Lagrangian for the Kaluza-Klein scalar and gauge fields arising from the dimensional reduction is considered. It is shown that the propagator of the scalar field associated to the determinant of the metric of the extra dimensions is strongly suppressed. This is an interesting result as in standard Kaluza-Klein theory this scalar degree of freedom is responsible for the constraint on the gauge fields which makes it impossible to recover the usual Yang-Mills equations. Moreover in the large D limit it turns out that the ultraviolet divergences due to the interactions between gauge and scalar fields are softened.

In this essay, we see how prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime) can lead to elegant proofs of number theoretical concepts. We namely develop the notion of primary units in a cyclotomic field, demonstrate their equivalence to real units in this case, and show how this leads to a proof of a special case of Fermat's Last Theorem. We finally modernize Dirichlet's solution to Pell's Equation.

Bell System Technical Journal, 14: 2. April 1935 pp 273-284. An Application of Number Theory to the Splicing of Telephone Cables. (Lawther, H.P., Jr.)

We have recently extended many-body perturbation theory and coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the restoration of the angular momentum at any truncation order [T. Duguet, J. Phys. G: Nucl. Part. Phys. 42 (2015) 025107]. Following a similar route, we presently extend Bogoliubov many-body perturbation theory and Bogoliubov coupled cluster theory performed on top of a Bogoliubov reference state breaking global gauge symmetry to allow for the restoration of the particle number at any truncation order. Eventually, formalisms can be merged to handle $SU(2)$ and $U(1)$ symmetries at the same time. Several further extensions of the newly proposed many-body formalisms can be foreseen in the mid-term future. The long-term goal relates to the ab initio description of near-degenerate finite quantum systems with an open-shell character.

We have recently extended many-body perturbation theory and coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the restoration of the angular momentum at any truncation order [T. Duguet, J. Phys. G: Nucl. Part. Phys. 42 (2015) 025107]. Following a similar route, we presently extend Bogoliubov many-body perturbation theory and Bogoliubov coupled cluster theory performed on top of a Bogoliubov reference state breaking global gauge symmetry to allow for the restoration of the particle number at any truncation order. Eventually, formalisms can be merged to handle $SU(2)$ and $U(1)$ symmetries at the same time. Several further extensions of the newly proposed many-body formalisms can be foreseen in the mid-term future. The long-term goal relates to the ab initio description of near-degenerate finite quantum systems with an open-shell character.

357, 98 p., 7 leaves of plates : 23 cm

357, 98 p., 7 leaves of plates : 23 cm

357, 98 p., 7 leaves of plates : 23 cm

357, 98 p., 7 leaves of plates : 23 cm

357, 98 p., 7 leaves of plates : 23 cm

There is a significant omission in the literature concerning the historical origins of the community college and the social and educational forces that have shaped its mission. Rigorous historical studies are relatively rare in higher education. For community colleges, analytical histories are even less common (Ratcliff, 1987; Frye, 1991, 1992). This study is a multidisciplinary historical analysis of the national junior-community college mission debate in the twentieth century. It combines fresh historical research with organization theory and consensus social movement theory to clarify and contextualize the community college mission and organizational behavior. The study explains the mission as an historically contingent social and educational process driven by a complex interaction of environmental pressures, institutional structure, organizational culture, and community and student demands.

This unit begins the second part of the course, in which we will investigate a class of methods in analytic number theory known as sieves. (For non-native speakers of English: in ordinary life, a sieve is a device through which you pour a powder, like �our, to �lter out large impurities.) Whereas the �rst part of the course leaned heavily on methods from complex analysis, here the emphasis will be more combinatorial.

This unit begins the second part of the course, in which we will investigate a class of methods in analytic number theory known as sieves. (For non-native speakers of English: in ordinary life, a sieve is a device through which you pour a powder, like �our, to �lter out large impurities.) Whereas the �rst part of the course leaned heavily on methods from complex analysis, here the emphasis will be more combinatorial.

This unit begins the second part of the course, in which we will investigate a class of methods in analytic number theory known as sieves. (For non-native speakers of English: in ordinary life, a sieve is a device through which you pour a powder, like �our, to �lter out large impurities.) Whereas the �rst part of the course leaned heavily on methods from complex analysis, here the emphasis will be more combinatorial.

This paper concerns the description of holomorphic extensions of algebraic number fields. We define a hyperbolized adele class group for every number field K Galois over Q and consider the Hardy space H[K] of graded-holomorphic functions on the hyperbolized adele class group. We show that the hyperplane N[K] in the projectivization PH[K] defined by the functions of non-zero trace possesses two partially-defined operations + and x, with respect to which there is canonical monomorphism of K into N[K]. We call N[K] a nonlinear field extension of K. We define Galois groups for nonlinear fields and show that Gal(N[L]/N[K]) is isomorphic to Gal(L/K) if L/K is Galois. If Q^{ab} denotes the maximal abelian extension of Q, C(Q) the idele class group and $\bar{N}[Q^{ab}]=PH[K] is the full projectivization, then there are embeddings of C(Q) into Gal_{+}(\bar{N}[Q^{ab}]/Q) and Gal_{x}(\bar{N}[Q^{ab}]/Q), the "Galois groups" of automorphisms preserving + resp. x only.

2 v. in 1 (xi, 274, [2], 275-576 p.) : 22 cm

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Allama Iqbal Library, University Of Kashmir Date Accessioned: 9/11/2015 15:58 The Digital Library of India was a project under the auspices of the Government of India.

Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.

In this unit, we introduce some special multiplicative functions, the Dirichlet characters, and study their corresponding Dirichlet series. We will use these in a subsequent unit to prove Dirichlet�s theorem on primes in arithmetic progressions, and the prime number theorem in arithmetic progressions.

In this unit, we introduce some special multiplicative functions, the Dirichlet characters, and study their corresponding Dirichlet series. We will use these in a subsequent unit to prove Dirichlet�s theorem on primes in arithmetic progressions, and the prime number theorem in arithmetic progressions.

In this unit, we introduce some special multiplicative functions, the Dirichlet characters, and study their corresponding Dirichlet series. We will use these in a subsequent unit to prove Dirichlet�s theorem on primes in arithmetic progressions, and the prime number theorem in arithmetic progressions.

For a CM abelian extension $F/K$ of an arbitrary totally real number field $K$, we construct the Stickelberger splitting maps (in the sense of \cite{Ba1}) for both the \'etale and the Quillen $K$--theory of $F$ and we use these maps to construct Euler systems in the even Quillen $K$--theory of $F$. The Stickelberger splitting maps give an immediate proof of the annihilation of the groups of divisible elements $div K_{2n}(F)_l$ of the even $K$--theory of the top field by higher Stickelberger elements, for all odd primes $l$. This generalizes the results of \cite{Ba1}, which only deals with CM abelian extensions of $\Bbb Q$. The techniques involved in constructing our Euler systems at this level of generality are quite different from those used in \cite{BG1}, where an Euler system in the odd $K$--theory with finite coefficients of abelian CM extensions of $\Bbb Q$ was given. We work under the assumption that the Iwasawa $\mu$--invariant conjecture holds. This permits us to make use of the recent results of Greither-Popescu \cite{GP} on the \'etale Coates-Sinnott conjecture for arbitrary abelian extensions of totally real number fields, which are conditional upon this assumption. In upcoming work, we will use the Euler systems constructed in this paper to obtain information on the groups of divisible elements $div K_{2n}(F)_l$, for all $n>0$ and odd $l$. It is known that the structure of these groups is intimately related to some of the deepest unsolved problems in algebraic number theory, e.g. the Kummer-Vandiver and Iwasawa conjectures on class groups of cyclotomic fields. We make these connections explicit in the introduction.

This is the first of three papers introducing a paradigm within which global algebraic number theory for the reals may be formulated so as to make possible the synthesis of algebraic and transcendental number theory into a coherent whole. We introduce diophantine approximation groups and their associated Kronecker foliations, using them to provide new algebraic and geometric characterizations of K-linear and algebraic dependence. As a consequence we find reformulations -- as algebraic and geometric (graph) rigidities -- of the Theorems of Baker and Lindemann-Weierstrass, the Logarithm Conjecture and the Schanuel Conjecture. There is an Appendix describing diophantine approximation groups as model theoretic types.

"Number Theory: 208-210" is an article from The American Mathematical Monthly, Volume 21 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2972989

"Number Theory: 208-210" is an article from The American Mathematical Monthly, Volume 21 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2972989

"Number Theory: 208-210" is an article from The American Mathematical Monthly, Volume 21 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2972989

This study investigates the relationship between executive functions, the number of siblings, and Theory of Mind (ToM) performance in German preschoolers. Prior research has consistently demonstrated that children with more advanced executive function (EF) skills tend to perform better on ToM tasks (e.g. Fujita et al., 2022). In addition to these cognitive factors, the social environment, particularly the number of siblings has also been shown to influence ToM development positively (Shahaeian et al., 2011). Based on these findings, the present study aims to examine whether executive functions and the number of siblings independently predict children's ToM performance, and whether there is an interaction between these two predictors. Specifically, we hypothesize that both EF and the number of siblings will be positively associated with ToM abilities, and that the effect of EF on ToM may be moderated by sibling count. Children will complete standardized tasks designed to assess their executive functions and Theory of Mind. Demographic information, including the number of siblings, age, and gender, will also be collected.

This study investigates the relationship between executive functions, the number of siblings, and Theory of Mind (ToM) performance in German preschoolers. Prior research has consistently demonstrated that children with more advanced executive function (EF) skills tend to perform better on ToM tasks (e.g. Fujita et al., 2022). In addition to these cognitive factors, the social environment, particularly the number of siblings has also been shown to influence ToM development positively (Shahaeian et al., 2011). Based on these findings, the present study aims to examine whether executive functions and the number of siblings independently predict children's ToM performance, and whether there is an interaction between these two predictors. Specifically, we hypothesize that both EF and the number of siblings will be positively associated with ToM abilities, and that the effect of EF on ToM may be moderated by sibling count. Children will complete standardized tasks designed to assess their executive functions and Theory of Mind. Demographic information, including the number of siblings, age, and gender, will also be collected.

The heat trace asymptotics on the noncommutative torus, where generalized Laplacians are made out of left and right regular representations, is fully determined. It turns out that this question is very sensitive to the number-theoretical aspect of the deformation parameters. The central condition we use is of a Diophantine type. More generally, the importance of number theory is made explicit on a few examples. We apply the results to the spectral action computation and revisit the UV/IR mixing phenomenon for a scalar theory. Although we find non-local counterterms in the NC $\phi^4$ theory on $\T^4$, we show that this theory can be made renormalizable at least at one loop, and may be even beyond.

The restoration of particle number within Energy Density Functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and non-projected densities. As an alternative that might be advantageous for mass models, nuclear dynamics and thermodynamics, we propose to formulate the functional in terms directly of the one-body and two-body density matrices of the state with good particle number. Our approach does not contain the pathologies recently observed when restoring the particle number in an Energy Density Functional framework based on transition density matrices and can eventually be applied with functionals having arbitrary density dependencies.

Based on some ideas introduced by Benci and Cerami \cite{benci-cerami_calvar}, we obtain an abstract result that establishes a version of the Morse relations. Afterward, we use this result to prove multiplicity of solutions for a nonlinear Schr\"odinger equation with an external magnetic field.

Based on some ideas introduced by Benci and Cerami \cite{benci-cerami_calvar}, we obtain an abstract result that establishes a version of the Morse relations. Afterward, we use this result to prove multiplicity of solutions for a nonlinear Schr\"odinger equation with an external magnetic field.

We present a quantum version of the classical probabilistic algorithms $\grave{a}$ la Rabin. The quantum algorithm is based on the essential use of Grover's operator for the quantum search of a database and of Shor's Fourier transform for extracting the periodicity of a function, and their combined use in the counting algorithm originally introduced by Brassard et al. One of the main features of our quantum probabilistic algorithm is its full unitarity and reversibility, which would make its use possible as part of larger and more complicated networks in quantum computers. As an example of this we describe polynomial time algorithms for studying some important problems in number theory, such as the test of the primality of an integer, the so called 'prime number theorem' and Hardy and Littlewood's conjecture about the asymptotic number of representations of an even integer as a sum of two primes.