Combinatorial problems are often easy to state and hard to solve. A whole bunch of graph coloring problems falls into this class as well as the satisfiability problem. The classical coloring problems consider colorings of objects such that two objects which are in a relation receive different colors, e.g., proper vertex-colorings, proper edge-colorings, or proper face-colorings of plane graphs....

Asymptotic extremal combinatorics deals with questions that in the language of model theory can be re-stated as follows. For finite models M, N of an universal theory without constants and function symbols (like graphs, digraphs or hypergraphs), let p(M, N) be the probability that a randomly chosen sub-model of N with |M | elements is isomorphic to M . Which asymptotic relations exist between t...

Gauss mixtures are a popular class of models in statistics and statistical signal processing because they can provide good £ts to smooth densities, because they have a rich theory, and because the can be well estimated by existing algorithms such as the EM algorithm. We here extend an information theortic extremal property for source coding from Gaussian sources to Gauss mixtures using high rat...

in this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)d^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the banach algebras. this proof is given in two cases of the continuous and discontinuous function $g$, under the generalized lipschitz and caratheodory conditions.

We study the Regge trajectories and the quark-antiquark energy in excited hadrons composed by different dynamical mass constituents via the gauge/string correspondence. First we exemplify the procedure in a supersymmetric system, D3-D7, in the extremal case. Afterwards we discuss the model dual to large-Nc QCD, D4-D6 system. In the latter case we find the field theory expected gross features of...

We study the “flat” directions of non-BPS extremal black hole attractors for N = 2, d = 4 supergravities whose vector multiplets’ scalar manifold is endowed with homogeneous symmetric special Kähler geometry. The non-BPS attractors with non-vanishing central charge have a moduli space described by real special geometry (and thus related to the d = 5 parent theory), whereas the moduli spaces of ...

we establish some relative volume comparison theorems for extremal volume forms of‎ ‎finsler manifolds under suitable curvature bounds‎. ‎as their applications‎, ‎we obtain some results on curvature and topology of finsler manifolds‎. ‎our results remove the usual assumption on s-curvature that is needed in the literature‎.

We extend the analysis of N=2 extremal Black-Hole attractor equations to the case of special geometries based on homogeneous coset spaces. For non-BPS critical points (with non vanishing central charge) the (Bekenstein-Hawking) entropy formula is the same as for symmetric spaces, namely four times the square of the central charge evaluated at the critical point. For non homogeneous geometries t...

In N=2 ungauged supergravity we have found the most general doubleextreme dyonic black holes with arbitrary number nv of constant vector multiplets and nh of constant hypermultiplets. They are double-extreme: 1) supersymmetric with coinciding horizons, 2) the mass for a given set of quantized charges is extremal. The spacetime is of the Reissner-Nordström form and the vector multiplet moduli de...

Multivariate regular variation describes the relative decay rates of joint tail probabilities of a random vector with respect to tail probabilities of a norm (any norm) of this random vector, and it is often used in studying heavy-tail phenomena observed in data analysis in various fields, such as finance and insurance. Multivariate regular variation can be analyzed in terms of the intensity me...