Semisymmetric prime-valent graphs of order $$2p^3$$ 2 p 3

Journal of Algebraic Combinatorics - A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime and $$\Gamma $$ a...     

On 2-transitive 3-nets

A 3-net is said to be 2-transitive if it admits a group of direction-preserving automorphisms fixing one of the transversal lines and acting 2-transitively on its points. We classify the 2-transitive finite 3-nets which do not admit a proper 2-transitive 3-subnet, except, possibly, for a subnet of order 2. The result is then extended under a weaker assumption.To Prof. Walter Benz and Prof. Jakob Joussen on their 60^th birthdaywork done within the activity of GNSAGA of CNR and supported by the Italian Ministry for Research and Technology.     

Some 3-Generator, 3-Relation Finite 2-Groups

Using computational methods, we first show that there are exactly eighteen 3-generator 2-groups of order 2¹⁰ with trivial Schur multiplier all having deficiency zero. We next generalize one of the groups obtained to exhibit two infinite classes of 3-generator, 3-relation finite 2-groups of high nilpotency class providing an affirmative answer to a problem posed by Havas et al.     

Synthesis of 3 : 4 dihydro 2H-pyrano (2, 3-b) quinolines

The synthesis of 3 : 4 dihydro 2H-pyrano(2, 3-b) quinolines is described.     

3-Rewritable Nilpotent 2-Groups of Class 2#

ABSTRACT

Let n be an integer greater than 1. A group G is said to be n-rewritable (or a Q_n-group) if for every n elements x₁, x₂,…,x_n in G there exist distinct permutations σ and τ in S_n such that x_σ(1)x_{σ (2)} ??? x_σ(n) = x_τ(1)x_τ(2) ??? x_τ(n). In this paper, we characterize all 3-rewritable nilpotent 2-groups of class 2. Also we have found a bound for the nilpotency class of certain nilpotent 3-rewritable groups, and have shown that 3-rewritable groups satisfy a certain law.     

Weitere Untersuchungen über die ternäre biquadratische Formf =x 1 3 x 2+x 2 3 x 3+x 3 3 x 1

Ohne Zusammenfassung     

Some q-analogues of supercongruences for truncated $$_3F_2$$ 3 F 2 hypergeometric series

The Ramanujan Journal - In this paper, we give an estimate of the lower bounds of the least common multiple of $$a,a+b,\ldots ,a+kb$$ for $$(a,b)=1,k\in \textit{N}^+$$ . Precisely, we prove that...     

Stable rank-2 vector bundles on ℙ3 withc 1=0 andc 2=3

Mathematische Annalen -     

2-Type surfaces in S 3

It is proved that the Riemannian product of two plane circles of different radii are the only compact surfaces of the 3-spheres in R ⁴ which can be constructed in R ⁴ by using eigenfunctions associated with two different eigenvalues of their corresponding Laplacians.     

三阶复正交矩阵与二阶矩阵代数上的相似变换

设M_2是二阶复矩阵的全体,Φ是M_2上的线性映射.本文建立了三阶复正交矩阵与M_2上的相似变换之间的一一对应关系,并利用这一对应关系证明了Φ保Lie积行列式(谱、边缘谱)的充要条件是存在c∈{±1,±i},二阶可逆矩阵T和二阶矩阵S,使得Φ(A)=cTAT~(-1)+tr(SA)I对所有A∈M_2都成立.     

Countable decompositions ofR 2 andR 3

If the continuum hypothesis holds,R ² is the union of countably many sets, none spanning a right triangle. Some partial results are obtained concerning the following conjecture of the first author:R ² is the union of countably many sets, none spanning an isosceles triangle. Finally, it is shown thatR ³ can be colored with countably many colors with no monochromatic rational distance.     

关于不定方程组x-1=3py^2，x^2＋x＋1=3z^2

设P为素数，利用同余及高次丢番图方程的一些结果证明了不定方程组x-1=3py^2，x^2＋x＋1=3z^2仅有正整数解（p，x，y，z）=（7，22，1，13）。     

Family of Pearson discrete distributions generated by the univariate hypergeometric function 3F2(α1, α2, α3; γ1, γ2; λ)

In this work we present a study of the Pearson discrete distributions generated by the hypergeometric function ₃F₂(α₁, α₂, α₃;γ₁, γ₂; λ), a univariate extension of the Gaussian hypergeometric function, through a constructive methodology. We start from the polynomial coefficients of the difference equation that lead to such a function as a solution. Immediately after, we obtain the generating probability function and the differential equation that it satisfies, valid for any admissible values of the parameters. We also obtain the differential equations that satisfy the cumulants generating function, moments generating function and characteristic function, From this point on, we obtain a relation in recurrences between the moments about the origin, allowing us to create an equation system for estimating the parameters by the moment method. We also establish a classification of all possible distributions of such type and conclude with a summation theorem that allows us study some distributions belonging to this family. © 1997 by John Wiley & Sons, Ltd.     

The Hankel Convolution and the Zemanian Spaces βμ and β'μ

In this paper we give structure theorems for the elements of the Zemanian spaces β'_μ and β'_μ,a' Also, bounded sets and convergent sequences in β'_μ,a' are characterized through representations as derivatives of measurable functions. Finally, we analyze the Hankel convolution on the above spaces.     

Semiorders and the 1/3–2/3 conjecture

A well-known conjecture of Fredman is that, for every finite partially ordered set (X, <) which is not a chain, there is a pair of elements x, y such that P(x, the proportion of linear extensions of (X, <) with x below y, lies between 1/3 and 2/3. In this paper, we prove the conjecture in the special case when (X, <) is a semiorder. A property we call 2-separation appears to be crucial, and we classify all locally finite 2-separated posets of bounded width.     

Combinatorially fruitful properties of 3⋅2 and 3⋅2 modulo p

Write a≡3⋅2⁻¹ and where p is an odd prime. Let c be a value that is congruent (modp) to either a or b. For any x from Z_p?{0}, evaluate each of x and within the interval (0,p). Then consider the quantity where the differences are evaluated in the interval (0,p−1), and the quantity where the differences are evaluated (modp+1) in the interval (0,p+1). As x varies over Z_p?{0}, the values of each of and give exactly two occurrences of nearly every member of 1,2,…,(p−1)/2. This fact enables a and b to be used in constructing some terraces for Z_p−1 and Z_p+1 from segments of elements that are themselves initially evaluated in Z_p.