Geometric Consequences Research Articles

Spectroscopic and Computational Investigation of the H155A Variant of Cysteine Dioxygenase: Geometric and Electronic Consequences of a Third-Sphere Amino Acid Substitution.

Cysteine dioxygenase (CDO) is a mononuclear, non-heme iron(II)-dependent enzyme that utilizes molecular oxygen to catalyze the oxidation of l-cysteine (Cys) to cysteinesulfinic acid. Although the kinetic consequences of various outer-sphere amino acid substitutions have previously been assessed, the effects of these substitutions on the geometric and electronic structures of the active site remained largely unexplored. In this work, we have performed a spectroscopic and computational characterization of the H155A CDO variant, which was previously shown to display a rate of Cys oxidation ∼100-fold decreased relative to that of wild-type (WT) CDO. Magnetic circular dichroism and electron paramagnetic resonance spectroscopic data indicate that the His155 → Ala substitution has a significant effect on the electronic structure of the Cys-bound Fe(II)CDO active site. An analysis of these data within the framework of density functional theory calculations reveals that Cys-bound H155A Fe(II)CDO possesses a six-coordinate Fe(II) center, differing from the analogous WT CDO species in the presence of an additional water ligand. The enhanced affinity of the Cys-bound Fe(II) center for a sixth ligand in the H155A CDO variant likely stems from the increased level of conformational freedom of the cysteine-tyrosine cross-link in the absence of the H155 imidazole ring. Notably, the nitrosyl adduct of Cys-bound Fe(II)CDO [which mimics the (O2/Cys)-CDO intermediate] is essentially unaffected by the H155A substitution, suggesting that the primary role played by the H155 side chain in CDO catalysis is to discourage the binding of a water molecule to the Cys-bound Fe(II)CDO active site.

Almost maximal growth of the Hilbert function

Let A=S/J be a standard artinian graded algebra over the polynomial ring S. A theorem of Macaulay dictates the possible growth of the Hilbert function of A from any degree to the next, and if this growth is the maximal possible then strong consequences have been given by Gotzmann. It can be phrased in terms of the base locus of the linear system defined by the relevant component(s) of J. If J is the artinian reduction of the ideal of a finite set of points in projective space then this maximal growth for A was shown by Bigatti, Geramita and the second author to imply strong geometric consequences for the points. We now suppose that the growth of the Hilbert function is one less than maximal. This again has (not as) strong consequences for the base locus defined by the relevant component. And when J is the artinian reduction of the ideal of a finite set of points in projective space, we prove that almost maximal growth again forces geometric consequences.

Geometric and energetic consequences of prototropy for adenine and its structural models – a review

Prototropy for adenine and its convenient models causes parallel changes of geometric (HOMED) and energetic (ΔE) parameters for neutral tautomers.

The 𝐬-Eulerian polynomials have only real roots

We study the roots of generalized Eulerian polynomials via a novel approach. We interpret Eulerian polynomials as the generating polynomials of a statistic over inversion sequences. Inversion sequences (also known as Lehmer codes or subexcedant functions) were recently generalized by Savage and Schuster, to arbitrary sequences s \mathbf {s} of positive integers, which they called s \mathbf {s} -inversion sequences. Our object of study is the generating polynomial of the ascent statistic over the set of s \mathbf {s} -inversion sequences of length n n . Since this ascent statistic over inversion sequences is equidistributed with the descent statistic over permutations, we call this generalized polynomial the s \mathbf {s} -Eulerian polynomial. The main result of this paper is that, for any sequence s \mathbf {s} of positive integers, the s \mathbf {s} -Eulerian polynomial has only real roots. This result is first shown to generalize several existing results about the real-rootedness of various Eulerian polynomials. We then show that it can be used to settle a conjecture of Brenti, that Eulerian polynomials for all finite Coxeter groups have only real roots, and partially settle a conjecture of Dilks, Petersen, Stembridge on type B affine Eulerian polynomials. It is then extended to several q q -analogs. We show that the MacMahon–Carlitz q q -Eulerian polynomial has only real roots whenever q q is a positive real number, confirming a conjecture of Chow and Gessel. The same holds true for the hyperoctahedral group and the wreath product groups, confirming further conjectures of Chow and Gessel, and Chow and Mansour, respectively. Our results have interesting geometric consequences as well.

On a certain duality of Néron-Severi lattices of supersingular K3 surfaces

Let X and Y be supersingular K3 surfaces defined over an algebraically closed field. Suppose that the sum of their Artin invariants is 11. Then there exists a certain duality between their Neron–Severi lattices. We investigate geometric consequences of this duality. As an application, we classify genus one fibrations on supersingular K3 surfaces with Artin invariant 10 in characteristic 2 and 3, and give a set of generators of the automorphism group of the nef cone of these supersingular K3 surfaces. The difference between the automorphism group of a supersingular K3 surface X and the automorphism group of its nef cone is determined by the period of X. We define the notion of genericity for supersingular K3 surfaces in terms of the period, and prove the existence of generic supersingular K3 surfaces in odd characteristics for each Artin invariant larger than one.

A geometric model of plaque incision and graft for Peyronie's disease with geometric analyses of different techniques.

A surgical approach with plaque incision and graft (PIG) to correct Peyronie's disease is the best method for complex, large deviations. However, the geometric and mechanical consequences of this intervention are poorly understood. The aim of this study was to analyze the geometric and mechanical consequences of PIG on penile straighten surgery. A tridimensional penile simile model with a curvature of 85° was created to test all of the most common PIG techniques. PIG with double-Y, H-shape, and Egydio techniques were used to rectify the curved penile model. The results that differed from a rectified cylinder shape were highlighted. All of the analyzed techniques created a geometric distortion that could be linked to poor surgical results. We suggest a new technique to resolve these abnormalities. Current techniques designed to correct penile deviation using PIG present geometric and mechanical imperfections with potential consequences to the postoperative success rate. The new technique proposed in this report could be a possible solution to solve the geometric distortion caused by PIG.

The Geometry of Cubic Polynomials

SummaryWe study the critical points of a complex cubic polynomial, normalized to have the form p(z) = (z - 1)(z - r1)(z - r2) with |r1| = 1 |r2|. If Tγ denotes the circle of diameter passing through 1 and 1 - γ, then there are α, β ∈ [0, 2] such that one critical point of p lies on Tα and the other on Tβ. We show that Tβ is the inversion of Tα over T1, from which many geometric consequences can be drawn. For example, (1) a critical point of such a polynomial almost always determines the polynomial uniquely, and (2) there is a “desert” in the unit disk, the open disk {z ϵ 핔 : |z - ⅔| < ⅓}, in which critical points cannot occur.

Tetra-μ3-iodido-tetra-kis-[(tri-n-butyl-phosphane-κP)copper(I)

The title complex, [Cu4I4(C12H27P)4], crystallizes with six mol­ecules in the unit cell and with three independent one-third mol­ecule fragments, completed by application of the relevant symmetry operators, in the asymmetric unit. The tetranuclear copper core shows a tetrahedral geometry (site symmetry 3..). The I atoms also form a tetra­hedron, with I⋯I distances of 4.471 (1) Å. Both tetra­hedra show an orientation similar to that of a pair of self-dual platonic bodies. The edges of the I-tetra­hedral structure are capped to the face centers of the Cu-tetra­hedron and vice versa. The Cuface⋯I distances are 2.18 Å (averaged) and the Iface⋯Cu distances are 0.78 Å (averaged). As a geometric consequence of these properties there are eight distorted trigonal–bipyramidal polyhedra evident, wherein each trigonal face builds up the equatorial site and the opposite Cu⋯I positions form the axial site. As expected, the n-butyl moieties are highly flexible, resulting in large elongations of their anisotropic displacement parameters. Some C atoms of the n-butyl groups were needed to fix alternative discrete disordered positions.

The influence of pre-adsorbed Pt on hydrogen adsorption on B2 FeTi(111)

The hydrogen adsorption properties on a Pt covered Fe-terminated B2-FeTi (111) surface are studied using the Density Functional Theory (DFT). The calculations are employed to trace relevant orbital interactions and to discuss the geometric and electronic consequences of incorporating one Pt atom or a Pt monolayer on top of the FeTi surface. The most stable adsorption site is a distorted FCC hollow for one Pt atom and from this location we build the Pt monolayer (ML). The H-adsorption energy is very close among BRIDGE, HCP and FCC hollow sites (∼−0.45 eV) being lower for the TOP site (−0.34 eV) in the case of a Pt(111) fcc surface. In the case of a Pt ML/FeTi, the H more stabilized on a BRIDGE site (∼−1.13 eV) interacting with both a Pt and Fe atom. We also computed the density of states (DOS) and the overlap population density of states (OPDOS) in order to study the evolution of the chemical bonding after adsorption.

Remarks on some starlike functions

Let A be the class of functions that are analytic in the unit disk D = {z ∈ C : |z| <1 } and normalized by f (0) = f � (0) – 1 = 0. In this work we investigate conditions under which |zf � (z)/f (z )– δ| < δ. Next we also estimate |Arg{f � (z)/z}|, |Arg{f (z)/z 2 }| and |Arg{zf � (z)/f (z)}| for functions of the form f (z )= z 2 + a3z 3 + ··· in the unit disc |z| <1 , which satisfy |f �� (z )–2 | < 2. Furthermore, some geometric consequences of these results are given. MSC: Primary 30C45; secondary 30C80

Local Constraints Satisfied by Realizable Correlation Functions

The Wiener-Khintchine theorem dictates that the correlation function of any stationary, stochastic signal y(t) has as its Fourier transform a function that is necessarily both real and non-negative. In this paper, I explore the real-space, geometric consequences of this reciprocal-space non-negativity constraint. I review prior results addressing this issue, and I also introduce a family of new, local constraints—each a consequence of the reciprocal-space non-negativity constraint—that are satisfied by the differentiable correlation functions.

Altered Mitral Inflow Orifice in Severe Aortic Regurgitation: Real Time Three-Dimensional Echocardiographic Findings

We present the case of a young man with severe eccentric aortic regurgitation, obstructing mitral inflow and provoking an audible Austin Flint murmur at clinical examination. Two-dimensional color Doppler echocardiography depicts the remarkable mechanical interaction between aortic regurgitant jet and anterior mitral leaflet opening. Three-dimensional transesophageal echocardiography aids in understanding the geometric and hemodynamic consequences of the regurgitant jet and in the genesis of the Austin Flint murmur. This case accentuates the incremental value of three-dimensional echocardiography when evaluating valvular pathology, and offers more insight in the interaction between aortic regurgitant flow and mitral leaflet dynamics.

Determination of the Effective Energy due to a Constant Modification in General Relativity

In this letter, we firstly discuss the geometric consequences of the resultant field equations in a specified f(R) theory of gravity. Afterwards, keeping the so called field equations separated, we investigate the analytical behavior of the effective energy, corresponding to our peculiar modification.

About the Calabi problem: a finite-dimensional approach

Let us consider a projective manifold M^n and a smooth volume form \Omega on M . We define the gradient flow associated to the problem of \Omega -balanced metrics in the quantum formalism, the \Omega -balancing flow. At the limit of the quantization, we prove that (see Theorem 1) the \Omega -balancing flow converges towards a natural flow in Kähler geometry, the \Omega -Kähler flow. We also prove the long time existence of the \Omega -Kähler flow and its convergence towards Yau's solution to the Calabi conjecture of prescribing the volume form in a given Kähler class (see Theorem 2). We derive some natural geometric consequences of our study.

Complex consequences: Substituent effects on metal⋯arylmethylium interactions

Metal complexation to aryl (Ph, Cp, cyclobutadienyl) methylium cations, radicals, and anions was investigated using hybrid density functional theory methods (B3LYP/LANL2DZ), with a focus on the effects of substituents. The results of these calculations, in which both geometric and energetic consequences of adding substituents were examined, indicate that metal–methylium interactions are most sensitive to substituent effects for complexed cations.

Algebraic geometry of Abel differential equation

A solution $$y(x)$$ of an Abel differential equation $$(1) \ y^{\prime }=p(x)y^2 + q(x) y^3$$ is called “closed” on $$[a,b]$$ if $$y(a)=y(b)$$ . The equation $$(1)$$ is said to have a center on $$[a,b]$$ if all its solutions (with the initial value $$y(a)$$ small enough) are closed. The problems of counting closed solutions (Smale–Pugh problem) is strongly related to the classical Hilbert 16th problem of bounding the number of limit cycles of a plane polynomial vector field. In turn, the problem of giving conditions on $$(p,q,a,b)$$ for $$(1)$$ to have a center on $$[a,b]$$ is analogous to the classical Poincare center–focus problem for plane vector fields. It is well known that both in the classical and in the Abel equation cases the center conditions are given by an infinite system of polynomial equations in the parameter space. The complexity of this system presents one of the main difficulties in the center–focus problem, as well as in the bounding of closed trajectories. In recent years two important structures have been related to the center equations for $$(1)$$ : composition algebra and moment vanishing. In the present paper we give an overview of these results (sometimes providing also new ones), stressing their algebraic–geometric interpretation and consequences. The second part of the paper is devoted to a rather detailed study of a specific example of the Abel equation which possesses algebraic solutions. We identify complex closed solutions, stressing their ramification properties. In particular, we analyze the continuation paths along which these solutions become closed.

Monotonicity and its analytic and geometric implications

In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of function spaces and the geometry of the underlining spaces are intertwined. After briefly discussing some of the well-known analytical applications of monotonicity for parabolic operators, we turn to their elliptic counterparts, their geometric meaning, and some geometric consequences.

The Symplectic Topology of Projective Manifolds with Small Dual

We study smooth projective varieties with small dual variety using methods from symplectic topology. We prove the affine parts of such varieties are subcritical, and that the hyperplane class is invertible in their quantum cohomology. We derive several topological and algebraic geometric consequences from that. The main tool in our work is the Seidel representation associated to Hamiltonian fibrations.

Critical Brownian sheet does not have double points

We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An $N$-parameter Brownian sheet in $\mathbf{R}^d$ has double points if and only if $d<4N$. In particular, in the critical case where $d=4N$, the Brownian sheet does not have double points. This answers an old problem in the folklore of the subject. We also discuss some of the geometric consequences of the mentioned decoupling, and establish a partial result concerning $k$-multiple points in the critical case $k(d-2N)=d$.

GENERALIZED β-CONFORMAL CHANGE AND SPECIAL FINSLER SPACES

This work is a continuation of the paper [Generalized beta-conformal change of Finsler metrics, Int. J. Geom. Meth. Mod. Phys. 7(4) (2010) 565–582]. In the present paper, we investigate the change of Finsler metrics [Formula: see text] which we refer to as a generalized β-conformal change. Under this change, we study some special Finsler spaces, namely, quasi-C-reducible, semi-C-reducible, C-reducible, C2-like, S3-like and S4-like Finsler spaces. We obtain some characterizations of the energy β-change, the Randers change and the Kropina change. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized β-conformal change, which we call the b-condition, and investigate the geometric consequences of such a condition. Finally, we give the conditions under which a generalized β-conformal change is projective and generalize some known results in the literature.