Let M be a circle or a compact interval, and let α “ k ` τ ě 1 be a real number such that k “ tαu. We write Diff`pMq for the group of orientation preserving Ck diffeomorphisms of M whose kth derivatives are Hölder continuous with exponent τ. We prove that there exists a continuum of isomorphism types of finitely generated subgroups G ď Diff`pMq with the property that G admits no injective homom...

In a recent paper with L. Q. Zamboni, the authors introduced the class of θ-episturmian words. An infinite word over A is standard θepisturmian, where θ is an involutory antimorphism of A∗, if its set of factors is closed under θ and its left special factors are prefixes. When θ is the reversal operator, one obtains the usual standard episturmian words. In this paper, we introduce and study θ-c...

Injective one-way trapdoor functions are one of the most fundamental cryptographic primitives. In this work we show how to derandomize lossy encryption (with long messages) to obtain lossy trapdoor functions, and hence injective one-way trapdoor functions. Bellare, Halevi, Sahai and Vadhan (CRYPTO ’98) showed that if Enc is an IND-CPA secure cryptosystem, and H is a random oracle, then x 7→ Enc...

In 1973, Greibach (“The hardest context-free language”, SIAM J. Comp., 1973) constructed a language L0 with the property that every can be reduced to by homomorphism, thus representing it as an inverse homomorphic image h−1(L0). this paper, similar characterization is established for family of grammars equipped operators referring left context any substring, recently defined Barash and Okhotin ...

We develop some aspects of the homological algebra persistence modules, in both one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. consider module sheaf tensor product Hom bifunctors well their derived functors, Tor Ext, give explicit computations for interval a classification injective, projective, flat state Kunneth theo...

The pure-injective R-modules are defined easily enough: as those modules which are injective over all pure embeddings, where an embedding A → B is said to be pure if every finite system of R-linear equations with constants from A and a solution in B has a solution in A. But the definition itself gives no indication of the rich theory around purity and pure-injectivity. The purpose of this surve...

Semigroups S for which the Banach algebra ℓ 1 (S) is injective are investigated and an application to the work of O. Yu. Aristov is described.

The local multiplier C*-algebra Mloc(A) of any C*-algebra A can be ∗-isomorphicly embedded into the injective envelope I(A) of A in such a way that the canonical embeddings of A into both these C*-algebras are identified. If A is commutative then Mloc(A) ≡ I(A). The injective envelopes of A and Mloc(A) always coincide, and every higher order local multiplier C*-algebra of A is contained in the ...

An injective $k$-edge-coloring of a graph $G$ is an assignment colors, i.e. integers in $\{1, \ldots , k\}$, to the edges such that any two each incident with one distinct endpoint third edge, receive colors. The problem determining whether $k$-coloring exists called k-INJECTIVE EDGE-COLORING. We show 3-INJECTIVE EDGE-COLORING NP-complete, even for triangle-free cubic graphs, planar subcubic gr...

This paper characterizes the injective and projective objects in the category of directed multigraphs, or quivers. Further, the injective envelope and projective cover of any quiver in this category is constructed.