Sequence Stratigraphy of the Fatha Formation in Shaqlawa Area, Northern Iraq

A surface section of the Fatha Formation (Middle Miocene) was studied in the Shaqlawa area, Erbil, Northern Iraq. It consists of siliciclastic silt, evaporates, and carbonates in a mixed siliciclastic silt composition. The Fatha Formation in the study area can be divided into two members of variable thickness based on rocky differences. Depositional settings ranged from shallow open-marine and restricted-hypersaline to supratidal and continental (sabkha, fluvio-deltaic, and exposure). It is bounded below by a type one sequence boundary above the Eocene Pila Spi Formation and marked by conglomerates. The upper sequence boundary with the Injana Formation is conformable. Thirteen sedimentary facies were distinguished in the Fatha Formation within the Shaqlawa region of northern Iraq and include sandstone to mudstone, wavy bedded sandstone to mudstone, Flaser bedded sandstone to mudstone, Marl, sandstone, cross lamination sandstone, Trough cross bedded sandstone, Planar cross bedded sandstone, marly limestone lithofacies, bioclastic grainstone to packstone microfacies, bioclastic lime mudstone to wackestone microfacies, lime mudstone-wackestone microfacies, and gypsum lithofacies. The depositional environment of the formation was inferred based on the facies association concepts. The succession formation can be divided into several third-order cycles, which reflect fluctuations in the relative sea-level rise. High-frequency cycles of transgressive System Tract and Highstand System tract. Fundamental to the evolution of the sequence, in this case, is the local tectonic component.

PRINCIPAL RADICAL SYSTEMS, LEFSCHETZ PROPERTIES, AND PERFECTION OF SPECHT IDEALS OF TWO-ROWED PARTITIONS

We show that the Specht ideal of a two-rowed partition is perfect over an arbitrary field, provided that the characteristic is either zero or bounded below by the size of the second row of the partition, and we show this lower bound is tight. We also establish perfection and other properties of certain variants of Specht ideals, and find a surprising connection to the weak Lefschetz property. Our results, in particular, give a self-contained proof of Cohen–Macaulayness of certain h-equals sets, a result previously obtained by Etingof–Gorsky–Losev over the complex numbers using rational Cherednik algebras.

Heegaard Floer Homology, Degree-One Maps and Splicing Knot Complements

Suppose that K and K' are knots inside the homology spheres Y and Y', respectively. Let X = Y (K, K') be the 3-manifold obtained by splicing the complements of K and K' and Z be the three-manifold obtained by 0 surgery on K. When Y' is an L-space, we use the splicing formula of [1] to show that the rank of (X ) is bounded below by the rank of (Y ) if τ(K 2) = 0 and is bounded below by rank( (Z)) − 2 rank( (Y)) + 1 if τ(K') ≠ 0.

Complete Logarithmic Sobolev inequality via Ricci curvature bounded below II

We study the “geometric Ricci curvature lower bound”, introduced previously by Junge, Li and LaRacuente, for a variety of examples including group von Neumann algebras, free orthogonal quantum groups [Formula: see text], [Formula: see text]-deformed Gaussian algebras and quantum tori. In particular, we show that Laplace operator on [Formula: see text] admits a factorization through the Laplace–Beltrami operator on the classical orthogonal group, which establishes the first connection between these two operators. Based on a non-negative curvature condition, we obtain the completely bounded version of the modified log-Sobolev inequalities for the corresponding quantum Markov semigroups on the examples mentioned above. We also prove that the “geometric Ricci curvature lower bound” is stable under tensor products and amalgamated free products. As an application, we obtain a sharp Ricci curvature lower bound for word-length semigroups on free group factors.

Conditions for the Existence of Absolutely Optimal Portfolios

Let Δn be the n-dimensional simplex, ξ = (ξ1, ξ2,…, ξn) be an n-dimensional random vector, and U be a set of utility functions. A vector x*∈ Δn is a U -absolutely optimal portfolio if EuξTx*≥EuξTx for every x ∈ Δn and u∈ U. In this paper, we investigate the following problem: For what random vectors, ξ, do U-absolutely optimal portfolios exist? If U2 is the set of concave utility functions, we find necessary and sufficient conditions on the distribution of the random vector, ξ, in order that it admits a U2-absolutely optimal portfolio. The main result is the following: If x0 is a portfolio having all its entries positive, then x0 is an absolutely optimal portfolio if and only if all the conditional expectations of ξi, given the return of portfolio x0, are the same. We prove that if ξ is bounded below then CARA-absolutely optimal portfolios are also U2-absolutely optimal portfolios. The classical case when the random vector ξ is normal is analyzed. We make a complete investigation of the simplest case of a bi-dimensional random vector ξ = (ξ1, ξ2). We give a complete characterization and we build two dimensional distributions that are absolutely continuous and admit U2-absolutely optimal portfolios.

Weaving Frames in Hilbert C ∗ -Modules

In this paper, we investigate weaving frames in Hilbert C ∗ -modules. We show that the equivalence of woven and weakly woven frames is still true for modular frames under certain conditions. By using the analysis operators of frames and frame operators of canonical duals, we obtain several perturbation results for given weaving frames and different weaving frame pairs. When the C ∗ -algebra is nonunital, we derive a correspondence of adjointable operators which is bounded below woven families. Finally, we discuss the redundancy of weaving frames in Hilbert C ∗ -modules.

Optimal transport maps on Alexandrov spaces revisited

We give an alternative proof for the fact that in n-dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely $$(n-1)$$ ( n - 1 ) -unrectifiable starting measure, and that this plan is induced by an optimal map. Our proof does not rely on the full optimality of a given plan but rather on the c-monotonicity, thus we obtain the existence of transport maps for wider class of (possibly non-optimal) transport plans.

Binomial edge ideals of unicyclic graphs

Let [Formula: see text] be a connected graph on the vertex set [Formula: see text]. Then [Formula: see text]. In this paper, we prove that if [Formula: see text] is a unicyclic graph, then the depth of [Formula: see text] is bounded below by [Formula: see text]. Also, we characterize [Formula: see text] with [Formula: see text] and [Formula: see text]. We then compute one of the distinguished extremal Betti numbers of [Formula: see text]. If [Formula: see text] is obtained by attaching whiskers at some vertices of the cycle of length [Formula: see text], then we show that [Formula: see text]. Furthermore, we characterize [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text]. In each of these cases, we classify the uniqueness of the extremal Betti number of these graphs.

An alternative approach to study irrotational periodic gravity water waves

We are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.