Alpha decay half-lives of superheavy nuclei 104 ≤ Z ≤ 125

In order to describe scattering, fusion, fission and ground state masses, Krappe and collaborators developed unified nuclear potential, by generalizing liquid drop model. They have incorporated phenomenological parameters accounting for the attractive force between two separated fragments. One of the phenomenological parameters involved in this model is the range of folded Yukawa function, which accounts for surface diffuseness of the potential and short range attractive interaction. The role of range of folding function of Yukawa-plus-exponential potential is analyzed for alpha decay of heavy and superheavy nuclei. Significant effect of this function is noted in preformation probability which improves the accuracy of half-lives of alpha decay. Half-lives for alpha decay are better obtained for two values of the range of folding function 0.54 and 0.8[Formula: see text]fm for heavy and superheavy mass regions, respectively. The study confirms the associated shell structure [Formula: see text] in heavy nuclei and [Formula: see text] and [Formula: see text] in superheavy nuclei. The calculations are extended to predict the half-lives of superheavy nuclei with [Formula: see text] and [Formula: see text] which are not yet synthesized experimentally.

On second non-HLC degree of closed symplecitc manifold

In this note, we show that for a closed almost-Kähler manifold [Formula: see text] with the almost complex structure [Formula: see text] satisfies [Formula: see text] the space of de Rham harmonic forms is contained in the space of symplectic-Bott–Chern harmonic forms. In particular, suppose that [Formula: see text] is four-dimensional, if the self-dual Betti number [Formula: see text], then we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott–Chern harmonic forms.

Pseudofinite groups and VC-dimension

We develop “local NIP group theory” in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure [Formula: see text] expanding a group, and left invariant NIP formula [Formula: see text], we prove various aspects of “local fsg” for the right-stratified formula [Formula: see text]. This includes a [Formula: see text]-type-definable connected component, uniqueness of the pseudofinite counting measure as a left-invariant measure on [Formula: see text]-formulas and generic compact domination for [Formula: see text]-definable sets.

Structure and Substructure Connectivity of Hypercube-Like Networks

The connectivity of a graph [Formula: see text], [Formula: see text], is the minimum number of vertices whose removal disconnects [Formula: see text], and the value of [Formula: see text] can be determined using Menger’s theorem. It has long been one of the most important factors that characterize both graph reliability and fault tolerability. Two extensions to the classic notion of connectivity were introduced recently: structure connectivity and substructure connectivity. Let [Formula: see text] be isomorphic to any connected subgraph of [Formula: see text]. The [Formula: see text]-structure connectivity of [Formula: see text], denoted by [Formula: see text], is the cardinality of a minimum set [Formula: see text] of connected subgraphs in [Formula: see text] such that every element of [Formula: see text] is isomorphic to [Formula: see text], and the removal of [Formula: see text] disconnects [Formula: see text]. The [Formula: see text]-substructure connectivity of [Formula: see text], denoted by [Formula: see text], is the cardinality of a minimum set [Formula: see text] of connected subgraphs in [Formula: see text] whose removal disconnects [Formula: see text] and every element of [Formula: see text] is isomorphic to a connected subgraph of [Formula: see text]. The family of hypercube-like networks includes many well-defined network architectures, such as hypercubes, crossed cubes, twisted cubes, and so on. In this paper, both the structure and substructure connectivity of hypercube-like networks are studied with respect to the [Formula: see text]-star [Formula: see text] structure, [Formula: see text], and the [Formula: see text]-cycle [Formula: see text] structure. Moreover, we consider the relationships between these parameters and other concepts.

On the complexity of the lattices of subvarieties and congruences

We find sufficient conditions guaranteeing that for a quasivariety [Formula: see text] of structures of finite type containing a [Formula: see text]-class with respect to [Formula: see text], there exists a subquasivariety [Formula: see text] and a structure [Formula: see text] such that the problems whether a finite lattice embeds into the lattice [Formula: see text] of [Formula: see text]-varieties and into the lattice [Formula: see text] are undecidable.

Visible-light photocatalytic activity of Fe@TiO2 core–shell composite synthesized by sol–gel method

Core–shell structure [Formula: see text] was synthesized by sol–gel method. The photocatalytic degradation of methylene blue over the [Formula: see text] reached 98% under UV light irradiation within 5 h. The band gap of the core–shell [Formula: see text] was found to have a redshift through a sintering treatment. The redshifted [Formula: see text] had a good performance of methylene-blue degradation (reaching 85%) under visible light irradiation for 5 h.

On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle

In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such algorithm is based in three properties that orthogonal polynomials satisfy: a recurrence relation, a structure formula, and a connection formula. This approach is used to obtain second-order differential equations whose solutions are orthogonal polynomials associated with some spectral transformations of a measure on the unit circle, as well as orthogonal polynomials associated with coherent pairs of measures on the unit circle.

Geometry from divergence functions and complex structures

Motivated by the geometrical structures of quantum mechanics, we introduce an almost complex structure [Formula: see text] on the product [Formula: see text] of any parallelizable statistical manifold [Formula: see text]. Then, we use [Formula: see text] to extract a pre-symplectic form and a metric-like tensor on [Formula: see text] from a divergence function. These tensors may be pulled back to [Formula: see text], and we compute them in the case of an N-dimensional symplex with respect to the Kullback–Leibler relative entropy, and in the case of (a suitable unfolding space of) the manifold of faithful density operators with respect to the von Neumann–Umegaki relative entropy.

Defining integer-valued functions in rings of continuous definable functions over a topological field

Let [Formula: see text] be an expansion of either an ordered field [Formula: see text], or a valued field [Formula: see text]. Given a definable set [Formula: see text] let [Formula: see text] be the ring of continuous definable functions from [Formula: see text] to [Formula: see text]. Under very mild assumptions on the geometry of [Formula: see text] and on the structure [Formula: see text], in particular when [Formula: see text] is [Formula: see text]-minimal or [Formula: see text]-minimal, or an expansion of a local field, we prove that the ring of integers [Formula: see text] is interpretable in [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] is definably connected of pure dimension [Formula: see text], then [Formula: see text] defines the subring [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] has no isolated points, then there is a discrete ring [Formula: see text] contained in [Formula: see text] and naturally isomorphic to [Formula: see text], such that the ring of functions [Formula: see text] which take values in [Formula: see text] is definable in [Formula: see text].

Weakly minimal groups with a new predicate

Fix a weakly minimal (i.e. superstable [Formula: see text]-rank [Formula: see text]) structure [Formula: see text]. Let [Formula: see text] be an expansion by constants for an elementary substructure, and let [Formula: see text] be an arbitrary subset of the universe [Formula: see text]. We show that all formulas in the expansion [Formula: see text] are equivalent to bounded formulas, and so [Formula: see text] is stable (or NIP) if and only if the [Formula: see text]-induced structure [Formula: see text] on [Formula: see text] is stable (or NIP). We then restrict to the case that [Formula: see text] is a pure abelian group with a weakly minimal theory, and [Formula: see text] is mutually algebraic (equivalently, weakly minimal with trivial forking). This setting encompasses most of the recent research on stable expansions of [Formula: see text]. Using various characterizations of mutual algebraicity, we give new examples of stable structures of the form [Formula: see text]. Most notably, we show that if [Formula: see text] is a weakly minimal additive subgroup of the algebraic numbers, [Formula: see text] is enumerated by a homogeneous linear recurrence relation with algebraic coefficients, and no repeated root of the characteristic polynomial of [Formula: see text] is a root of unity, then [Formula: see text] is superstable for any [Formula: see text].