Issue 2, Volume 47, June 2022

2022

1. Gromov’s Oka Principle, Fiber Bundles and the Conformal Module Burglind Jöricke PDF

   ▸ Abstract

   The conformal module of conjugacy classes of braids is an invariant that appeared earlier than the entropy of conjugacy classes of braids, and is inversely proportional to the entropy. Using the relation between the two invariants, we give a short conceptional proof of an earlier result on the conformal module. Mainly, we consider situations, when the conformal module of conjugacy classes of braids serves as obstruction for the existence of homotopies (or isotopies) of smooth objects involving braids to the respective holomorphic objects, and present theorems on the restricted validity of Gromov’s Oka principle in these situations.

   375-440
2. Jacquet-Mao Metaplectic Fundamental Lemma is Motivic Do Viet Cuong PDF

   ▸ Abstract

   We prove that all the ingredients of Jacquet-Mao’s fundamental belong to the class of so-called motivic exponential functions defined by means of a first-order language of logic. In an earlier paper, this fundamental lemma is proved for p-adic fields. As a consequence of the fact that all its ingredients are motivic functions, we obtain that the fundamental holds also for local function fields.

   441-456
3. Schmidt’s Subspace Theorem for Moving Hypersurface Targets in Subgeneral Position in Projective Varieties Giang Le PDF

   ▸ Abstract

   Our goal is to give Schmidt’s subspace theorem for moving hypersurface targets in subgeneral position in projective varieties.

   457-474
4. Some Results on Pure Ideals and Trace Ideals of Projective Modules Abolfazl Tarizadeh PDF

   ▸ Abstract

   Let $R$ be a commutative ring with the unit element. It is shown that an ideal $I$ in $R$ is pure if and only if $\mathrm{Ann}(f)+I=R$ for all $f\in I$. If $J$ is the trace of a projective $R$-module $M$, we prove that $J$ is generated by the “coordinates” of $M$ and $JM=M$. These lead to a few new results and alternative proofs for some known results.

   475-481
5. On Semiregular Endomorphism Rings and the Dual of Yamagata’s Theorem Tamer Koşan , Truong Cong Quynh PDF

   ▸ Abstract

   In this paper, we characterize a module whose endomorphism ring is $\delta$-semiregular. For a right $R$-module $M$, we also obtained dual Yamagata’s theorem on the set $\nabla_{\delta}=\{f\in End(M)|f(M) \text{ is } \delta \text{ small in } M\}$.

   483-493
6. A Note on Symmetric Elements of Division Rings with Involution Vo Hoang Minh Thu PDF

   ▸ Abstract

   Let D be a division ring with involution ⋆ and S the set of all symmetric elements of D. Assume that the center F of D is uncountable and K is a division subring of D containing F. The main aim of this note is to show that S is right algebraic over K if and only if so is D. This result allows us to construct an example of division rings K ⊂ D such that D is right algebraic but not left algebraic over K.

   495-502
7. Weighted Estimates for Vector-Valued Intrinsic Square Functions and Commutators in the Morrey-Type Spaces Hua Wang PDF

   ▸ Abstract

   In this paper, the boundedness properties of vector-valued intrinsic square functions and their vector-valued commutators with $BMO(\mathbb {R}^{n}) $ functions are discussed. We first show the weighted strong-type and weak-type estimates of vector-valued intrinsic square functions in the Morrey-type spaces. Then, we obtain weighted strong-type estimates of vector-valued analogues of commutators in Morrey-type spaces. In the endpoint case, we establish the weighted weak $L\log L $-type estimates for these vector-valued commutators in the setting of weighted Lebesgue spaces. Furthermore, we prove weighted endpoint estimates of these commutator operators in Morrey-type spaces. In particular, we can obtain strong-type and endpoint estimates of vector-valued intrinsic square functions and their commutators in the weighted Morrey spaces and the generalized Morrey spaces.

   503-537
8. General Variational Inequalities: Existence of Solutions, Tikhonov-Type Regularization, and Well-posedness Tran Van Nghi , Nguyen Nang Tam PDF

   ▸ Abstract

   In this paper, we present necessary and sufficient conditions for existence and uniqueness of solutions of general variational inequalities (GVIs). A Tikhonov-type regularization method to find a solution of GVIs is proposed. Finally, under suitable conditions, we prove that the well-posedness of a GVI is equivalent to the solution existence and uniqueness. The obtained results are compared with the previous ones. In particular, our results generalize corresponding ones for inverse variational inequalities.

   539-552
9. A Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Finding Fixed Points of a Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces Vahid Darvish , Kittisak Jantakarn , Anchalee Kaewcharoen , Nader Biranvand PDF

   ▸ Abstract

   In this paper, we study a new iterative method for finding fixed points of a weak Bregman relatively nonexpansive mapping and solutions of generalized mixed equilibrium problems in Banach spaces.

   553-569
10. Normality and Product of Spherical Derivatives Virender Singh , Banarsi Lal PDF

    ▸ Abstract

    In this paper, we prove some normality criteria involving product of spherical derivatives of a meromorphic function and that of its derivatives.

    571-579
11. Upper and Lower Bounds for Noncommutative Perspectives of Operator Monotone Functions: the Case of Second Variable Silvestru Sever Dragomir PDF

    ▸ Abstract

    Assume that the function $f:[0,\infty )\rightarrow \mathbb {R} $ is operator monotone in $[0,\infty )$. We can define the perspective $\mathcal {P}_{f}\left (B,A\right )$ by setting $$\mathcal{P}_{f}\left( B,A\right) :=A^{1/2}f\left( A^{-1/2}BA^{-1/2}\right) A^{1/2}, $$ where $A, B>0$. In this paper, we show among others that, if $\sigma \geq C \geq \rho>0$, $D>0$, $\varsigma\geq Q\geq\tau>0$ and $0<$$n\leq D-C\leq N$ for some constants $\rho, \sigma, \varsigma, \tau, n, N$, then $$\begin{array}{@{}rcl@{}} 0& \le& \frac{n}{N{\varsigma}^{2}}\left[ \mathcal{P}_{f}\left( {\varsigma} ,N+\sigma \right) -\mathcal{P}_{f}\left( {\varsigma} ,\sigma \right) \right] Q^{2} \\ & \leq& \mathcal{P}_{f}\left( Q,D\right) -\mathcal{P}_{f}\left( Q,C\right) \\ & \leq& \frac{N}{n\tau^{2}}\left[ \mathcal{P}_{f}\left( \tau ,n+\rho \right) -\mathcal{P}_{f}\left( \tau ,\rho \right) \right] Q^{2}. \end{array} $$ Applications for the weighted operator geometric mean and the perspective $$\mathcal{P}_{\ln \left( \cdot +1\right) }\left( B,A\right) :=A^{1/2}\ln \left( A^{-1/2}BA^{-1/2}+1\right) A^{1/2},~ A,B>0 $$ are also provided.

    581-595