Abstract. After Zagier proved that the traces of singular moduli j(z) are Fourier coefficients of a weakly holomorphic modular form, various properties of the traces of the singular values of modular functions mostly on the full modular group PSL2(Z) have been investigated such as their exact formulas, limiting distribution, duality, and congruences. The purpose of this paper is to generalize t...

In this paper, we prove a result of existence and uniqueness solutions for the following class problem initial value differential equations with maxima Caputo?s fractional order on time scales: c??a u(?) = ?(?, u(?), max ??[a,?] u(?)), ? J := [a, b]T, 0 < 1, u(a) ?, We used techniques Picard weakly operators to obtain some data dependency parameters results.

An analysis of wave front motion in weakly coupled doped semiconductor superlattices is presented. If a dimensionless doping is sufficiently large, the superlattice behaves as a discrete system presenting front propagation failure and the wave fronts can be described near the threshold currents J(i) (i=1,2) at which they depin and move. The wave front velocity scales with current as |J-J(i)|(1/...

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

In this paper, we study the uniqueness problems on meromorphic function and its k th order derivative. The results in this paper improve the results given by K. W. Yu (On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4(1)(2003), Art. 21), L. P. Liu and Y. X. Gu (Uniqueness of meromorphic functions that share one small function w...

Let G be a connected graph with vertex set V (G). A set S of vertices in G is called a weakly connected dominating set of G if (i) S is a dominating set of G and (ii) the graph obtained from G by removing all edges joining two vertices in V (G) \ S is connected. A weakly connected dominating set S of G is said to be minimum or a γw-set if |S| is minimum among all weakly connected dominating set...

We present a construction of a CCA2-secure encryption scheme from a plaintext aware, weakly simulatable public key encryption scheme. The notion of plaintext aware, weakly simulatable public key encryption has been considered previously by Myers, Sergi and shelat (SCN, 2012) and natural encryption schemes such as the Damg̊ard Elgamal Scheme (Damg̊ard, Crypto, 1991) and the Cramer-Shoup Lite Schem...

The notion of strict closedness rings was given by J. Lipman [Amer. Math. 93 (1971), pp. 649–685] in connection with a conjecture O. Zariski. present purpose is to give practical method construction strictly closed rings. It also shown that the Stanley-Reisner simplicial complexes (resp. $F$-pure satisfying condition $(\operatorname {S}_2)$ Serre) are weakly Arf)

In this paper, we classify all commutative weakly distance-regular digraphs of girth g and one type arcs under the assumption that \(p_{(1,g-1),(1,g-1)}^{(2,g-2)}\ge k_{1,g-1}-2\). consequence, Yang et al. (J Comb Theory Ser A 160:288–315, 2018, Theorem 1.1) is partially generalized by our result.

A Recently proposed Jπ = 1/2¯, J/Ψ Λ (PΛΨs) pentaquark structure at 4338.2 MeV/c2 is investigated using a first-order mass formula. This relationship based on weakly bound meson plus baryon clusters, and provides reasonable prediction (within about 1%) of the mass. The first order formula model predicts possible 1/2¯ 3/2¯ assignments for PΛΨs.