二部图形式的Erd\H{O}s-S\'{o}s猜想

二部图形式的Erd\H{O}s-S\''{o}s猜想     

An old conjecture of Erdos-Turán on additive bases

There is a 1941 conjecture of Erdos and Turán on what is now called additive basis that we restate:

Conjecture 0.1(Erdos and Turán). Suppose that is an increasing sequence of integers and

Suppose that

If 0$"> for all , then is unbounded.

Our main purpose is to show that the sequence cannot be bounded by . There is a surprisingly simple, though computationally very intensive, algorithm that establishes this.

     

一类整函数的牛顿法的拟直接盘和直接盘

In this paper, we consider Newton＇s method for a class of entire functions with infinite order. By using theory of dynamics of functions meromorphic outside a small set, we find there are some series of virtual immediate basins in which the dynamics converges to infinity and a series of immediate basins with finite area in the Fatou sets of Newton＇s method.     

某些Ruzsa数$R_m$的新上界

For A ■ Z m and n ∈ Z m ,let σ A (n) be the number of solutions of equation n = x + y,x,y ∈ A.Given a positive integer m,let R m be the least positive integer r such that there exists a set A ■ Z m with A + A = Z m and σ A (n) ≤ r.Recently,Chen Yonggao proved that all R m ≤ 288.In this paper,we obtain new upper bounds of some special type R kp 2 .     

线性超图的边染色

超图$H$的一个$k$-边染色是用$k$种颜色的边染色, 使得相交的边染不同的颜色. Erd\H{o}s-Faber-Lov\''asz猜想认为任一$n$个顶点的无环线性超图都有一个$n$-边染色. 2021年, Kang, Kelly, K\"uhn, Methuku和Osthus对充分大的$n$确认了该猜想成立. 在本文中, 我们证明该猜想对弱冲突的超图是成立的. 这严格拓展了Bretto, Faisant 和Hennecart在2020年的两个相关结果.     

Borel subrings of the reals

A Borel (or even analytic) subring of either has Hausdorff dimension or is all of . Extensions of the method of proof yield (among other things) that any analytic subring of having positive Hausdorff dimension is equal to either or .

     

Asymptotics of recurrence coefficients for orthonormal polynomials on the line--Magnus's method revisited

We use Freud equations to obtain the main term in the asymptotic expansion of the recurrence coefficients associated with orthonormal polynomials for weights on the real line where is an even polynomial of fixed degree with nonnegative coefficients or where . Here for some real -1$">.

     

Stability of a stochastic SEIS model with saturation incidence and latent period

In this paper, a stochastic SEIS epidemic model with a saturation incidence rate and a time delay describing the latent period of the disease is investigated. The model inherits the endemic steady state from its corresponding deterministic counterpart. We first show the existence and uniqueness of the global positive solution of the model. Then, by constructing Lyapunov functionals, we derive sufficient conditions ensuring the stochastic stability of the endemic steady state. Numerical simulations are carried out to confirm our analytical results. Furthermore, our simulation results shows that the existence of noise and delay may cause the endemic steady state to be unstable.     

The Mardesic factorization theorem for extension theory and c-separation

We shall prove a type of Mardesic factorization theorem for extension theory over an arbitrary stratum of CW-complexes in the class of arbitrary compact Hausdorff spaces. Our result provides that the space through which the factorization occurs will have the same strong countability property (e.g., strong countable dimension) as the original one had. Taking into consideration the class of compact Hausdorff spaces, this result extends all previous ones of its type. Our factorization theorem will simultaneously include factorization for weak infinite-dimensionality and for Property C, that is, for C-spaces.

A corollary to our result will be that for any weight and any finitely homotopy dominated CW-complex , there exists a Hausdorff compactum with weight and which is universal for the property and weight . The condition means that for every closed subset of and every map , there exists a map which is an extension of . The universality means that for every compact Hausdorff space whose weight is and for which is true, there is an embedding of into .

We shall show, on the other hand, that there exists a CW-complex which is not finitely homotopy dominated but which has the property that for each weight , there exists a Hausdorff compactum which is universal for the property and weight .

     

Analysis of a stochastic two-predators one-prey system with modified Leslie-Gower and Holling-type II schemes

In this paper, we consider a stochastic two-predators one-prey model with modified Leslie-Gower and Holling-type II schemes. Analytically, we completely classify the parameter space into eight categories containing eleven cases. In each case, we show that every population is either stable in time average or extinct, depending on the parameters of the model. Finally, we work out some simulation figures to illustrate the theoretical results.     

Ladder operators for Szego polynomials and related biorthogonal rational functions

We find the raising and lowering operators for orthogonal polynomials on the unit circle introduced by Szego and for their four parameter generalization to biorthogonal rational functions on the unit circle.

     

Erratum to "More Results on Hermite-Hadamard type inequality through (α,m)-preinvexity"

In this paper, we present some corrections to definitions of $m$-preinvex, $\left( \alpha,m\right) $-preinvex functions and statements of the theorems of the results proved in [7].     

Fej\'{e}r type inequalities for Harmonically-convex functions with applications

In this paper, a new weighted identity involving harmonically symmetric functions and differentiable functions is established. By using the notion of harmonic symmetricity, harmonic convexity and some auxiliary results, some new Fej\''{e}r type integral inequalities are presented. Applications to special means of positive real numbers are given as well.