Compact Difference Schemes for the Multidimensional Klein–Gordon Equation

Differential Equations - Stable compact difference schemes of $$4+2$$ and $$4+4 $$ approximation orders are considered and studied on standard stencils for the multidimensional Klein–Gordon...     

On Stoll’s criterion for the maximality of quadratic arboreal Galois representations

Archiv der Mathematik - We show that for a quadratic polynomial $$f(x)=x^2-c$$ , where $$c=(8k+2)(8k+3)$$ or $$c=(4k+1)(4k+2)+1$$ with $$k\in {\mathbb {N}}\cup \{0\}$$ , the Galois group of the...     

On the Nonexistence of Distance-Regular Graphs with Intersection Array $$ \{ 53,40,28,16; 1,4,10,28\}$$

Journal of Applied and Industrial Mathematics - We consider $$Q$$ -polynomial graphs of diameter $$4 $$ . Alongside the infinite series of intersection arrays $$ \{m(2m+1),(m-1)(2m+1),m^2, m;...     

二项式系数的更多整除性质

设$a$, $b$和$n$为正整数,且$a>b$,我们证明了下面的整除性质: 对所有正整数$n$, 我们有$$(2bn+1)(2bn+3)(2bn+5){2bn\choose bn}\Big|15(a-b)(3a-b)(5a-b)(5a-3b){2an \choose an}{an\choose bn},$$ 上述整除式推广了杨全会一文中的相关结论.且对所有正整数$n$,我们证明了下面的整除性质:$$(6n+1){4n\choose n}\Big|{12n\choose 6n}{2n\choose n},\ (12n+1){5n\choose n}\Big|{15n\choose 3n}{3n-1\choose n-1},$$ $$(18n+1){12n\choose 9n}{8n\choose 2n}\Big| {24n\choose 18n}{4n\choose 2n}{6n\choose 3n}.$$更多类似的整除性质可以给出.     

Homogeneous non-degenerate 3-(α,δ)-Sasaki manifolds and submersions over quaternionic Kähler spaces

Annals of Global Analysis and Geometry - We show that every 3- $$(\alpha ,\delta )$$ -Sasaki manifold of dimension $$4n + 3$$ admits a locally defined Riemannian submersion over a quaternionic...     

An Lp-Lq-Version of Morgan’s Theorem for the Dunkl-Bessel Transform

In this paper, we give an L^p-L^q-version of Morgans theorem for the Dunkl-Bessel transform on More precisely, we prove that for all and then for all measurable function f on the conditions and imply f = 0, if and only if where are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004     

The depth of a reflexive polytope

Given arbitrary integers d and r with $$d \ge 4$$ and $$1 \le r \le d + 1$$ , a reflexive polytope $${\mathscr {P}}\subset {\mathbb R}^d$$ of dimension d with $$\mathrm{depth}\,K[{\mathscr {P}}] = r$$ for which its dual polytope $${\mathscr {P}}^\vee $$ is normal will be constructed, where $$K[{\mathscr {P}}]$$ is the toric ring of $${\mathscr {P}}$$ .     

Compact Difference Schemes on a Three-Point Stencil for Second-Order Hyperbolic Equations

Differential Equations - We consider compact difference schemes of approximation order $$4+2 $$ on a three-point spatial stencil for the Klein–Gordon equations with constant and variable...     

f-Laplace非线性方程的梯度估计和Liouville定理

设(M,g,e~(-f)dv_g)是n维完备光滑的度量测度空间.考虑以下非线性椭圆方程△_f~u+hu~α=0,1α(n+m)/(n+m-2)(n+m≥4)和非线性抛物方程(△_f-?/?t)u+hu~α=0,α0正解的梯度估计.对于经典的Laplace情形,Li (Li J. Gradient estimates and harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds [J]. J Funct Anal,1991, 100:233-256.)证明了正解的梯度估计和Liouville定理.在本文中,对于上述的f-Laplace方程,作者将推导出相应的结果.     

The equation $$x^4+2^ny^4=z^4$$ x 4 + 2 n y 4 = z 4 in algebraic number fields

Acta Mathematica Hungarica - Let n be a positive integer. We show that if the equation $$(1) \qquad \qquad \qquad x^4+2^ny^4=z^4$$ has a solution (x,y,z) in a cubic number field K with $$xyz \neq...     

On the Structure of Solutions of the Moisil-Théodoresco System in Euclidean Space

Let be open, let be the Dirac operator in and let be the Clifford algebra constructed over the quadratic space . If for fixed, denotes the space of r-vectors in , then an -valued smooth function W = W ^r  + W ^r+2 in Ω is said to satisfy the Moisil-Théodoresco system if . In terms of differential forms, this means that the corresponding - valued smooth form w = w ^r  + w ^r+2 satisfies in Ω the system d ^* w ^r = 0, dw ^r  + d ^* w ^r+2 = 0; dw ^r+2 = 0. Based on techniques and results concerning conjugate harmonic functions in the framework of Clifford analysis, a structure theorem is proved for the solutions of the Moisil-Théodoresco system.      

Characterization of distributive semigroup operations on the positive real numbers

Given any cancellative continuous semigroup operation $$\star $$ on the positive real numbers $$\mathbf {R}_+$$ with the ordinary topology, we completely characterize the set $$\mathcal {D}_\star (\mathbf {R}_+)$$ of all cancellative continuous semigroup operations on $$\mathbf {R}_+$$ which are distributed by $$\star $$ in terms of homeomorphism. As a consequence, we show that an arbitrary semigroup operation in $$\mathcal {D}_\star (\mathbf {R}_+)$$ is homeomorphically isomorphic to the ordinary addition $$+$$ on $$\mathbf {R}_+$$.     

Class number one problem for the real quadratic fields $${{\mathbb {Q}({\sqrt{m^2+2r}})}}$$ Q ( m 2 + 2 r )

Archiv der Mathematik - We investigate the class number one problem for a parametric family of real quadratic fields of the form $$\mathbb {Q}( \sqrt{m^2+4r})$$ for certain positive integers m and r.     

Optimal selection for good polynomials of degree up to five

Designs, Codes and Cryptography - An $$(r,\ell )$$ -good polynomial is a polynomial of degree $$r+1$$ that is constant on $$\ell $$ subsets of $$\mathbb F_q$$ , each of size $$r+1$$ . For any...     

Triangle in a triangle: On a problem of Steinhaus

A necessary and sufficient condition on the sidesp, q, r of a trianglePQR and the sidesa, b, c of a triangleABC in order thatABC contains a congruent copy ofPQR is the following: At least one of the 18 inequalities obtained by cyclic permutation of {a, b, c} and arbitrary permutation of {itp, q, r} in the formula $$\begin{array}{l} Max\{ F(q^2 + r^2 - p^2 ), F'(b^2 + c^2 - a^2 )\} \\ + Max\{ F(p^2 + r^2 - q^2 ), F'(a^2 + c^2 - b^2 )\} \le 2Fcr \\ \end{array}$$ is satisfied. In this formulaF andF′ denote the surface areas of the triangles, i.e. $$\begin{array}{l} F = {\textstyle{1 \over 4}}(2a^2 b^2 + 2b^2 c^2 + 2c^2 a^2 - a^4 - b^4 - c^4 )^{1/2} \\ F' = {\textstyle{1 \over 4}}(2p^2 q^2 + 2q^2 r^2 + 2r^2 p^2 - p^4 - q^4 - r^4 )^{1/2} . \\ \end{array}$$      

A parameterized family of quadratic class groups with 3-Sylow subgroups of rank at least three

The Ramanujan Journal - In a recent paper, Kishi and Komatsu have shown that the complex quadratic fields of discriminant $$\begin{aligned} \Delta _{18} = 4 - 3^{18n+3} \end{aligned}$$ have a class...     

On the Spectrum of a Non-Self-Adjoint Quasiperiodic Operator

Doklady Mathematics - We study the operator $$\mathcal{A}$$ acting in $${{l}^{2}}(\mathbb{Z})$$ by the formula $${{(\mathcal{A}u)}_{l}} = {{u}_{{l + 1}}} + {{u}_{{l - 1}}} + \lambda {{e}^{{ - 2\pi...     

On large equilateral point-sets in normed spaces

What is the largest cardinal of a two-by-two equilateral point-set in an n-dimensional Minkowski space? It is conjectured that this cardinal is at least $$n+1$$, and several spaces are tight in this regard, such as the Euclidean space. In this paper, we prove in normed spaces X with the $$(H_1,\dots ,H_{n-1})$$-2-intersection property the existence of $$n+1$$ equilateral point-sets of large diameter inscribed to the unit ball B. This extends the construction of Makeev (J Math Sci (N Y) 140:548–550, 2007) in dimension 4.     

Stable constant mean curvature hypersurfaces in the real projective space

In this paper, we prove that the only compact two-sided hypersurfaces with constant mean curvature H which are weakly stable in and have constant scalar curvature are (i) the twofold covering of a totally geodesic projective space; (ii) the geodesic spheres in ; and (iii) the quotient to of the hypersurface obtained as the product of two spheres of dimensions k and n − k, with k = 1,..., n − 1, and radii r and , respectively, with .