Related papers: A note on bifurcation theorems of Rabinowitz type
The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.
We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…
The paper is devoted to a generalized and improved version of author's approach to Gromov bounded cohomology theory. In particular, the awkward countability assumption is removed and the aspects related to homological algebra are clarified.…
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
We study the properties, in particular termination, of dependent types systems for lambda calculus and rewriting.
This note presents a unified theorem of the alternative that explicitly allows for any combination of equality, componentwise inequality, weak dominance, strict dominance, and nonnegativity relations. The theorem nests 60 special cases,…
The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].
The theorem on the existence of bifurcation points of the stationary solutions for the Vlasov-Maxwell system with bifurcation direction is proved.
In this paper, we introduce two primality tests based on new divisibility properties of binomial coefficients. These new properties were enunciated and proved in previous work. We also study two similar tests that can be obtained from…
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
In these notes we provide the foundation for the deformation theoretic parts of arXiv:0807.3753 and arXiv:math/0102005.
In recent years, the theory for Leibniz integral rule in the fractional sense has not been able to get substantial development. As an urgent problem to be solved, we study a Leibniz integral rule for Riemann-Liouville and Caputo type…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
The aim of this note is to discuss resolution theorems that are useful in the study of semi log canonical varieties.
There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.
From the viewpoint of semi-abelian homology, some recent results on homology of Leibniz n-algebras can be explained categorically. In parallel with these results, we develop an analogous theory for Lie n-algebras. We also consider the…
In this sequel to arxiv:arXiv:1012.0835 we develop Bezout type theorems for semidegrees (including an explicit formula for {\em iterated semidegrees}) and an inequality for subdegrees. In addition we prove (in case of surfaces) a Bernstein…
We give a presentation of abelian class field theory.
We outline the proofs of several principal statements in conventional renormalization theory. This may be of some use in the light of new trends and new techniques (Hopf algebras, etc.) recently introduced in the field.