Related papers: Counterexamples to Bloch's Principle and its Conve…
In this paper we continue our earlier investigations on normal families of meromorphic functions\cite{CS2}. Here, we prove some value distribution results which lead to some normality criteria for a family of meromorphic functions involving…
In this paper, we prove two normality criteria for a family of meromorphic functions. The first criterion extends a result of Fang and Zalcman[Normal families and shared values of meromorphic functions II, Comput. Methods Funct. Theory,…
In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for…
We prove a Zalcman-Pang lemma in several complex variables and apply it to obtain several complex variables analogues of the known normality criteria like Lappan's five-point theorem and Schwick's theorem.
In this paper we give a new proof, relying on Banach's contraction mapping principle, of a celebrated theorem of Andr\'e Bloch. Also, via the same contraction mapping principle, we give a proof of a Bloch type theorem for normalised Wu…
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
We give an example of $C^k$-integrable almost complex structure that does not admit a corresponding $C^{k+1}$-complex coordinate system.
We proove a Bloch's theorem in an almost complex projective plane.
In this paper, we first establish a Schwarz-Pick type theorem for pluriharmonic mappings and then we apply it to discuss the equivalent norms on Lipschitz-type spaces. Finally, we obtain several Landau's and Bloch's type theorems for…
A heuristic principle attributed to A. Bloch says that a family of holomorphic functions is likely to be normal if there is no nonconstant entire functions with this property. We discuss this principle and survey recent results that have…
We obtain analytical lower bounds on the concurrence of bipartite quantum systems in arbitrary dimensions related to the violation of separability conditions based on local uncertainty relations and on the Bloch representation of density…
In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.
In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.
In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J.…
Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that is not only commensurate with classical physics (as…
We estabish an analog of the Cauchy-Poincare separation theorem for normal matrices in terms of majorization. Moreover, we present a solution to the inverse spectral problem (Borg-type result) for a normal matrix. Using this result we…
Another counter-example to Dirac's Conjecture is presented, which resembles the Cawley model but is so modified as to include second class constraints. The arbitrary function in the general solution to the defining equations of momenta…
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas Theorem by using…
We introduce a geometric condition of Bloch type which guarantees that a subset of a bounded convex domain in several complex variables is degenerate with respect to every iterated function system. Furthermore we discuss the relations of…
In this paper we generalize a result of Ye, Pang and Yang[12] on the normality of a family of holomorphic curves in $P^N(\mathbb{C})$. Further we obtain a normality criterion for family of meromorphic functions that partially share…