We prove a complexity dichotomy theorem for class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function f=[x0,x1,x2,x3], we that the problem Holant(f|(=3)) is either computable in polynomial time or #P-hard. The criterion f explicit.

We prove the existence of solutions to the differential inclusion ẍ(t) ∈ F (x(t), ẋ(t)) + f(t, x(t), ẋ(t)), x(0) = x0, ẋ(0) = y0, where f is a Carathéodory function and F with nonconvex values in a Hilbert space such that F (x, y) ⊂ γ(∂g(y)), with g a regular locally Lipschitz function and γ a linear operator.

In this paper, we prove that a linear action of a reductive group on a polynomial ring with good ltrations over a eld of characteristic p > 0 yields a strongly F-regular (in particular, Cohen-Macaulay) invariant subring. The strongly F-regular property of some known examples of invariant subrings, such as the coordinate rings of Schubert varieties in Grassmannians, are recovered. A similar resu...

In this work we prove that the set of points at infinity S8 :“ ClRPm pSqXH8 of a semialgebraic set S Ă R that is the image of a polynomial map f : R Ñ R is connected. This result is no longer true in general if f is a regular map. However, it still works for a large family of regular maps that we call quasi-polynomial maps.

(1) Frobenius splitting in commutative algebra, Karen Smith and Wenliang Zhang. (2) A survey of test ideals, Karl Schwede and Kevin Tucker. (3) Globally F-regular and log Fano varities, Karl Schwede and Karen Smith. (4) Characterizations of regular local rings of characteristic p, Ernst Kunz. (5) On Noetherian rings of characteristic p, Ernst Kunz. (6) F-purity and rational singularity, Richard...

We consider a real analytic map-germ (f, g) : (R, 0) → (R, 0). Under some conditions, we establish degree formulas for the following quantities : χ({f = α} ∩ {g = δ} ∩B ε ), χ({f = α} ∩ {g ≥ δ} ∩B ε )− χ({f = α} ∩ {g ≤ δ} ∩B ε ), where (α, δ) is a regular value of (f, g) and 0 < |(α, δ)| ¿ ε ¿ 1.

Important properties such as differentiability and convexity of symmetric functions in Rn can be transferred to the corresponding spectral functions and vice-versa. Continuing to built on this line of research, we hereby prove that a spectral function F : Sn → R ∪ {+∞} is prox-regular if and only if the underlying symmetric function f : Rn → R ∪ {+∞} is prox-regular. Relevant properties of symm...

The local behavior of regular wavelet sampling expansions is quantified. The term “regular” refers to the decay properties of scaling functions φ of a given multiresolution analysis. The regularity of the sampling function corresponding to φ is proved. This regularity is used to determine small intervals of sampling points so that the sampled values of a signal f at this finite set of points gi...

be the set of affine critical values. The set Baff is a subset of B but is not necessarily equal to B. The value c ∈ C is regular at infinity if there exists a disk D centered at c and a compact set K of C2 with a locally trivial fibration f : f−1 (D) \K −→ D. There is only a finite number of non-regular values at infinity: the critical values at infinity collected in B∞. The bifurcation set B ...

In this paper we study the dynamics of regular polynomial automorphisms of C. These maps provide a natural generalization of complex Hénon maps in C to higher dimensions. For a given regular polynomial automorphism f we construct a filtration in C which has particular escape properties for the orbits of f . In the case when f is hyperbolic we obtain a complete description of its orbits. In the ...