Symmetry algebra of the AdS4×ℂℙ3 superstring

By direct calculation in the classical theory, we derive the central extension of the off-shell symmetry algebra for a string propagating in AdS ₄ ×?? ³ . It turns out to be the same as in the case of the AdS ₅ ×S ⁵ string. We consider the choice of the κ-symmetry gauge in detail and also explain how this gauge can be chosen without breaking the bosonic symmetries.     

Analytical Solution of Lamb’s Problem in the Case of a Limiting Poisson Ratio

Computational Mathematics and Mathematical Physics - Lamb’s problem for a force applied to the boundary of an elastic half-space is considered in the case of a limiting Poisson ratio of 1/2....     

Limiting behavior of relative Rényi entropy in a non-regular location shift family

We calculate the limiting behavior of relative Rényi entropy between adjacent two probability distribution in a non-regular location-shift family which is generated by a probability distribution whose support is an interval or a half-line. This limit can be regarded as a generalization of Fisher information, and seems closely related to information geometry and large deviation theory.     

Limiting behaviour of Fréchet means in the space of phylogenetic trees

As demonstrated in our previous work on \({\varvec{T}}_{\!4}\), the space of phylogenetic trees with four leaves, the topological structure of the space plays an important role in the non-classical limiting behaviour of the sample Fréchet means in \({\varvec{T}}_{\!4}\). Nevertheless, the techniques used in that paper cannot be adapted to analyse Fréchet means in the space \({\varvec{T}}_{\!m}\) of phylogenetic trees with \(m(\geqslant \!5)\) leaves. To investigate the latter, this paper first studies the log map of \({\varvec{T}}_{\!m}\). Then, in terms of a modified version of this map, we characterise Fréchet means in \({\varvec{T}}_{\!m}\) that lie in top-dimensional or co-dimension one strata. We derive the limiting distributions for the corresponding sample Fréchet means, generalising our previous results. In particular, the results show that, although they are related to the Gaussian distribution, the forms taken by the limiting distributions depend on the co-dimensions of the strata in which the Fréchet means lie.     

The rank of a 2 × 2 × 2 tensor

As computing power increases, many more problems in engineering and data analysis involve computation with tensors, or multi-way data arrays. Most applications involve computing a decomposition of a tensor into a linear combination of rank-1 tensors. Ideally, the decomposition involves a minimal number of terms, i.e. computation of the rank of the tensor. Tensor rank is not a straight-forward extension of matrix rank. A constructive proof based on an eigenvalue criterion is provided that shows when a 2?×?2?×?2 tensor over ? is rank-3 and when it is rank-2. The results are extended to show that n?×?n?×?2 tensors over ? have maximum possible rank n?+?k where k is the number of complex conjugate eigenvalue pairs of the matrices forming the two faces of the tensor cube.     

Minimal Self-Similar Peano Curve of Genus 5 × 5

Doklady Mathematics - The paper presents a plane regular fractal Peano curve with a Euclidean square-to-line ratio (L2-locality) of $$5frac{{43}}{{73}}$$ , which is minimal among all known curves...     

Four Classes of Surfaces with Constant Mean Curvature in S 3 × R and H 3 × R

Deforming rotation surfaces with constant mean curvature in S ³ and H ³ to S ³ × R and H ³ × R respectvely, we give four classes of surfaces with mean curvature vector of constant length in S ³ × R and H ³ × R. We have complete minimal surfaces in S ³ × R and H ³ × R. Also we obtain minimal 2-tori in S ³ × S ¹, some of which are embedded.     

On the Yamabe constants of S2×R3 and S3×R2

We compare the isoperimetric profiles of $S^2\times {\mathbb{R}}^3$ and of $S^3\times {\mathbb{R}}^2$ with that of a round 5-sphere (of appropriate radius). Then we use this comparison to obtain lower bounds for the Yamabe constants of $S^2\times {\mathbb{R}}^3$ and $S^3\times {\mathbb{R}}^2$. Explicitly we show that $Y(S^3\times {\mathbb{R}}^2,[g_0^3+d{x}^2])>(3/4)Y(S^5)$ and $Y(S^2\times {\mathbb{R}}^3,[g_0^2+d{x}^2])>0.63Y(S^5)$. We also obtain explicit lower bounds in higher dimensions and for products of Euclidean space with a closed manifold of positive Ricci curvature. The techniques are a more general version of those used by the same authors in Petean and Ruiz (2011) [15] and the results are a complement to the work developed by B. Ammann, M. Dahl and E. Humbert to obtain explicit gap theorems for the Yamabe invariants in low dimensions.     

Multiplicative Jordan Decomposition in Integral Group Ring of Group K_8×C_5

In this article,we present the multiplicative Jordan decomposition in integral group ring of group K8 × C5,where K8 is the quaternion group of order 8.Thus,we give a positive answer to the question raised by Hales A W,Passi I B S and Wilson L E in the paper "The multiplicative Jordan decomposition in group rings II.     

Characterizing Convexity of a Function by Its Fréchet and Limiting Second-Order Subdifferentials

The Fréchet and limiting second-order subdifferentials of a proper lower semicontinuous convex function \(\varphi: \mathbb R^n\rightarrow\bar{\mathbb R}\) have a property called the positive semi-definiteness (PSD)—in analogy with the notion of positive semi-definiteness of symmetric real matrices. In general, the PSD is insufficient for ensuring the convexity of an arbitrary lower semicontinuous function φ. However, if φ is a C ^1,1 function then the PSD property of one of the second-order subdifferentials is a complete characterization of the convexity of φ. The same assertion is valid for C ¹ functions of one variable. The limiting second-order subdifferential can recognize the convexity/nonconvexity of piecewise linear functions and of separable piecewise C ² functions, while its Fréchet counterpart cannot.     

Characterization of elements of polynomials in ��S

Given the discrete space of natural numbers, we characterize the elements of polynomials evaluated on the points of ???. We establish these results by proving the characterization in a far more general setting. Let S be a discrete set which is a semigroup under two operations ? and +. Let g(z ₁,z ₂,??,z _k ) be any polynomial and p ₁,p ₂,??,p _k be elements of ??S. We provide a sufficient condition that a set A?S is a member of g(p ₁,p ₂,??,p _k ) and use it to characterize the members of g(p ₁,p ₂,??,p _k ) if each p _i is an idempotent in (??S,+).     

A q-Analogue of the Stirling Formula and a Continuous Limiting Behaviour of the q-Binomial Distribution—Numerical Calculations

In this article, we derive an asymptotic formula for the q-factorial number of order n using the saddle point method. This formula is a q-analogue, for 0?<?q?<?1, of the usual Stirling formula for the factorial number of order n. Also, this formula is used to provide a continuous limiting behaviour of the q-Binomial distribution in the sense of pointwise convergence. Specifically, the q-Binomial distribution converges to a continuous Stieltjes–Wigert distribution. Furthermore, we present some numerical calculations, using the computer program MAPLE, indicating a quite strong convergence.     

On a Conjecture of S.Halperin

If X is a finite simply connected CW complex, then H_*(X,Q) is finitedimensional, let n_X = max{i|H_i(X,Q)≠0}. On the other hand,π_i(X) is the directsum of finitely many copies of Z and finite Abelian group. We call an interval[k,l] a torsion gap for X if π_k(X) and π_l (X) both coutain copies of Z, andπ_i (X)(k相似文献   

On a new family of complete G 2-holonomy Riemannian metrics on S 3 × ℝ4

Studying a system of first-order nonlinear ordinary differential equations for the functions determining a deformation of the standard conic metric over S ³ × S ³, we prove the existence of a one-parameter family of complete G ₂-holonomy Riemannian metrics on S ³ × ?⁴.