Let $$(A, {{\mathscr {L}}}, \Theta _n)$$ be a dimension g abelian variety together with level n theta structure over field k of odd characteristic. We thus denote by $$(\theta ^{\Theta _{{\mathscr {L}}}}_{i})_{(\mathbb {Z}/ \mathbb {Z})^g} \in \Gamma (A, {L}}})$$ the associated standard basis. For positive integer $$\ell $$ relatively prime to and characteristic k, we study change algorithms wh...

In this very short paper, we show that the average overlap density of a union-closed family $\mathcal{F}$ subsets $\{1,2,\ldots,n\}$ may be as small \[\Theta((\log_2 \log_2 |\mathcal{F}|)/(\log_2 |\mathcal{F}|)),\] for infinitely many positive integers $n$.

In a previous paper (see http:/www.math.ohio-state.edu/ ̃czorn/ works.html), we computed examples of the doubling integral for constituents of the unramified principal series of Sp2(F ) and S̃p2(F ) where F was a nondyadic field. These computations relied on certain “good test vectors” and “good theta test sections” motivated by the non-vanishing of theta lifts. In this paper, we aim to prove a p...

The lens, whose image height is proportional to its field view angle through introducing reasonable barrel distortion so as to scan or mark linearly is called F-theta lens. Design of F-theta lens is introduced in the paper. The design idea and method are illustrated in detail through the analysis of two systems with working area of 200×200mm and 500×500mm. They’re simple and compact. Both of th...

In this paper we give an explicit parameterization of the local theta correspondence of supercuspidal representations for the reductive dual pairs (U1(F ),U1(F )), (U1(F ),U1,1(F )), (U1(F ),U2(F )), and (U1(F ),U1,2(F )) of unitary groups over a nonarchimedean local field F of odd residue characteristic.

In this research paper, we concentrate on the existence and uniqueness of common fixed points various mappings in b2 metric space under generalized (ϕ,f)λ-expansive conditions implicit contractive conditions. Additionally, derive a progression noteworthy approaches ideas extending conclusions real to space, which advances investigation will be able advance.

Let (X, dX) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f : X → T such that for every x ∈ X, ED [ max y∈X\{x} dT ( f (x), f (y)) dX(x, y) ] ≤ C(log n), where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient...

Some new limit contractive conditions in fuzzy metric spaces are introduced, by using property (E.A), some common fixed point theorems for four maps are proved in GV-fuzzy metric spaces. As an application of our results, some new contractive conditions are presented, and some common fixed point theorems are proved under these contractive conditions. The contractive conditions presented in this ...

We study special cycles on integral models of Shimura varieties associated with unitary similitude groups of signature (n−1, 1). We construct an arithmetic theta lift from harmonic Maass forms of weight 2 − n to the arithmetic Chow group of the integral model of a unitary Shimura variety, by associating to a harmonic Maass form f a linear combination of Kudla– Rapoport divisors, equipped with t...

A major factor that affects solute and water transport through tissue is the state of tissue hydration. The amount of interstitial water directly affects the transport coefficients for both diffusion and convection. To investigate the effect of simultaneous exposure of tissue to hydrostatic and osmotic pressures on the state of tissue hydration and the pattern of distribution of tissue water, w...