We extend the usual world-volume action for a Dp-brane to the case of N coincident Dpbranes where the world-volume theory involves a U(N) gauge theory. The guiding principle in our construction is that the action should be consistent with the familiar rules of T-duality. The resulting action involves a variety of potential terms, i.e., nonderivative interactions, for the nonabelian scalar field...

DP-coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvořák and Postle. We introduce study (i,j)-defective DP-colorings simple graphs. Let gDP(i,j,n) be the minimum number edges in an n-vertex DP-(i,j)-critical graph. In this paper we determine sharp bound on for each i≥3 j≥2i+1 infinitely many n.

A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...

here, we have considered the husimi and wigner distribution functions. we have, inparticular, shown how the uncertainty principle works for the two cases of simple and damped harmonicoscillators when either of these two distributions are used. the conclusion shows that the husimidistribution function remains non-negative through the phase space but it does not always satisfies theuncertainty pr...

We partially generalize the known results on dp-minimal fields to dp-finite fields. prove a dichotomy: if K is sufficiently saturated expansion of field, then either has finite Morley rank or non-trivial Aut(K/A)-invariant valuation ring for some small set A. In positive characteristic case, we can even obtain henselian ring. Using this, classify pure

We prove that NIP valued fields of positive characteristic are henselian, and we begin to generalize the known results on dp-minimal dp-finite fields. On any unstable field K, define a type-definable group “infinitesimals,” corresponding canonical topology (K,+). reduce classification construction non-trivial Aut(K/A)-invariant valuation rings.

In his insightful editorial, Nir Eyal explores the connections between nudging and shaming. One upshot of his argument is that we should question the principle of the least restrictive alternative in public health and health policy. In this commentary, I maintain that Eyal’s argument undermines only a rather implausible version of the principle of the least restrictive alternative and I sketch ...

A new form of the discrepancy principle for Poisson inverse problems with compact operators is proposed and discussed in relation to various other proposals. It shown that filter-induced spectral regularization a priori chosen smoothing parameter produces estimators are rate-minimax under source conditions on estimated function. With used posteriori choice parameter, solutions consistent (in pr...