We consider the problem of uniform asymptotics in kernel functional estimation where the bandwidth can depend on the data. In a unified approach we investigate kernel estimates of the density and the hazard rate for uncensored and right-censored observations. The model allows for the fixed bandwidth as well as for various variable bandwidths, e.g. the nearest neighbor bandwidth. An elementary p...

‎In this paper‎, ‎we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves‎. ‎The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $‎, ‎is a straightforward generalization of elliptic curve Diffie-Hellman key exchange‎. ‎The method uses commutativity of the endomorphism ring $ End(E) $‎. ‎Then using dual isogenies‎, ‎we propose...

We introduce the notion of “maximal rank type” for representations of quivers, which requires certain collections of maps involved in the representation to be of maximal rank. We show that real root representations of quivers are of maximal rank type. By using the maximal rank type property and universal extension functors we construct all real root representations of a particular wild quiver w...

Let K,S,D be a division ring an endomorphism and a S-derivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Viète formula and decompositions of differential operators. W -polynomials show up naturally, their connections with P -independency, Vandermonde and Wronskian matrices are briefly studied. The different linear factorizations ...

We will show that the Dirichlet-to-Neumann map Λ for the electrical conductivity equation on a simply connected plane region has an alternating property, which may be considered as a generalized maximum principle. Using this property, we will prove that the kernel, K, of Λ satisfies a set of inequalities of the form (−1) n(n+1) 2 detK(xi, yj) > 0. We will show that these inequalities imply Hopf...

We discuss the existence of classes of quadratic time-frequency representations (QTFRs), e.g. Cohen, power, and generalized time-shift covariant, that satisfy a time-frequency (TF) concentration property. This important property yields perfect QTFR concentration along group delay curves. It also (1) simpli es the QTFR formulation and property kernel constraints as the kernel reduces from 2-D to...

We provide a condition for f -ergodicity of strong Markov processes at a subgeometric rate. This condition is couched in terms of a supermartingale property for a functional of the Markov process. Equivalent formulations in terms of a drift inequality on the extended generator and on the resolvent kernel are given. Results related to (f, r)-regularity and to moderate deviation principle for int...

We prove that the natural order on the idempotents of the endomorphism monoid of the countably in®nite random graph is d 0-universal; that is, it embeds every countable order. We therefore extend in a strong fashion a result of [2] which showed that the natural order embeds every countable linear order. We consider a re®nement of the natural order which embeds every countable quasi-order.

In this paper, we consider the Frobenius endomorphism on twisted Edwards curve and give the characteristic polynomial of the map. Applying the Frobenius endomorphism on twisted Edwards curve, we construct a skew-Frobenius map defined on the quadratic twist of an twisted Edwards curve. Our results show that the Frobenius endomorphism on twisted Edwards curve and the skew-Frobenius endomorphism o...

In this thesis we consider sequences of non-negative integers which arise from counting the periodic points of a map T : X → X, where X is a non-empty set. Some of the main results obtained are concerned with the counting of the periodic points of an endomorphism of a group, in particular when the group is locally nilpotent, for which class of groups a local-global property is established. The ...