Respect Tot Research Articles

Existence of nontrivial solutions for a quasilinear Schrödinger–Poisson system in $\mathbb{R}^3$ with periodic potentials

In this paper, we study the following quasilinear Schrödinger–Poisson system in R 3 { − Δ u + V ( x ) u + λ ϕ u = f ( x , u ) , x ∈ R 3 , − Δ ϕ − ε 4 Δ 4 ϕ = λ u 2 , x ∈ R 3 , where λ and ε are positive parameters, Δ 4 u = div ( | ∇ u | 2 ∇ u ) , V is a continuous and periodic potential function with positive infimum, f ( x , t ) ∈ C ( R 3 × R , R ) is periodic with respect to x and only needs to satisfy some superquadratic growth conditions with respect to t . One nontrivial solution is obtained for λ small enough and ε fixed by a combination of variational methods and truncation technique.

Equi-Lipschitz minimizing trajectories for non coercive, discontinuous, non convex Bolza controlled-linear optimal control problems

This article deals with the Lipschitz regularity of the “approximate” minimizers for the Bolza type control functional of the form \[ J t ( y , u ) ≔ ∫ t T Λ ( s , y ( s ) , u ( s ) ) d s + g ( y ( T ) ) J_t(y,u)≔\int _t^T\Lambda (s,y(s), u(s))\,ds+g(y(T)) \] among the pairs ( y , u ) (y,u) satisfying a prescribed initial condition y ( t ) = x y(t)=x , where the state y y is absolutely continuous, the control u u is summable and the dynamic is controlled-linear of the form y ′ = b ( y ) u y’=b(y)u . For b ≡ 1 b\equiv 1 the above becomes a problem of the calculus of variations. The Lagrangian Λ ( s , y , u ) \Lambda (s,y,u) is assumed to be either convex in the variable u u on every half-line from the origin (radial convexity in u u ), or partial differentiable in the control variable and satisfies a local Lipschitz regularity on the time variable, named Condition (S). It is allowed to be extended valued, discontinuous in y y or in u u , and non convex in u u . We assume a very mild growth condition, actually a violation of the Du Bois-Reymond–Erdmann equation for high values of the control, that is fulfilled if the Lagrangian is coercive as well as in some almost linear cases. The main result states that, given any admissible pair ( y , u ) (y,u) , there exists a more convenient admissible pair ( y ¯ , u ¯ ) (\overline y, \overline u) for J t J_t where u ¯ \overline u is bounded, y ¯ \overline y is Lipschitz, with bounds and ranks that are uniform with respect to t , x t,x in the compact subsets of [ 0 , T [ × R n [0,T[\times \mathbb {R}^n . The result is new even in the superlinear case. As a consequence, there are minimizing sequences that are formed by pairs of equi-Lipschitz trajectories and equi-bounded controls. A new existence and regularity result follows without assuming any kind of Lipschitzianity in the state variable. We deduce, without any need of growth conditions, the nonoccurrence of the Lavrentiev phenomenon for a wide class of Lagrangians containing those that satisfy Condition (S), are bounded on bounded sets “well” inside the effective domain and are radially convex in the control variable. The methods are based on a reparametrization technique and do not involve the Maximum Principle.

Generic semistability for reductive group actions

We prove that given a reductive algebraic group G G and a rational representation ρ : G → G L ( V ) \rho : G \to \mathrm {GL}(V) defined over an algebraically closed field of characteristic 0 0 , v ∈ V v \in V is generically semistable, i.e., 0 ∉ T . v ¯ 0 \not \in \overline {T.v} for a general maximal torus T T if and only if v v is semistable with respect to the induced action of the center of G G . The proof is obtained through a detailed description of the relation between the state polytope with respect to the maximal torus T T of G G and the state polytope with respect to T ∩ [ G , G ] T \cap [G,G] . We also consider the case of solvable groups and prove that the generic semistability implies the center semistability but not the other way around.

Positive associations between infections ofToxoplasma gondiiand seropositivity withAnisakis simplexin human patients suffering from chronic urticaria

Toxoplasma gondii is a food-borne and orofecal microorganism which produces chronic infection, and attempts have been made to prove its negative association with atopy in the context of the hygiene hypothesis. Anisakis simplex is a fish parasite associated with chronic urticaria (CU) in endemic regions. We analysed the relationship between both infectious agents in CU. We included 42 patients with chronic urticaria (18 patients with CU associated with A. simplex sensitization and 24 not sensitized CU patients). Patients were assessed for atopy by a skin prick test (SPT) against common aeroallergens and for respiratory symptoms. Anisakis simplex sensitization was assessed by SPT and specific IgE by CAP fluoro-enzyme immunoassay (CAP-FEIA). Anti-T. gondii IgG levels were measured by enzyme-linked immunosorbent assay (ELISA). CU patients were analysed with respect to T. gondii seropositivity, A. simplex sensitization, atopy and immigrant status. The seroprevalence of T. gondii was 40.5% in CU patients and 42.1% in the control group. Immigrants were more frequently infected by T. gondii (41.2% versus 12%; P =0.036). Anti-T. gondii IgG antibodies were associated with past A. simplex parasitism (odds ratio 6.73; P =0.03) and independently with atopic sensitization (odds ratio 5.85; P =0.04). In CU patients, T. gondii has no protective effect on atopic sensitization or A. simplex sensitization.

Long-Term Survival and Intracellular Replication of Mycoplasma hominis in Trichomonas vaginalis Cells: Potential Role of the Protozoon in Transmitting Bacterial Infection

The existence of a symbiotic relationship between Trichomonas vaginalis and Mycoplasma hominis, which is the first reported example of symbiosis between two obligate human pathogens, has been recently reported by our research group. In this work, we examined the cellular location of M. hominis in respect to T. vaginalis. By using gentamicin protection assays, double immunofluorescence, and confocal microscopy, we obtained strong evidence that M. hominis is located within protozoan cells. 5-Bromodeoxyuridine incorporation assays showed that intracellularly located mycoplasmas actively synthesize DNA. Our results demonstrate that M. hominis has the capability of entering trichomonad cells and of replicating inside the protozoon. These findings suggest that symbiosis might provide the bacteria, during human infection, with the capability to resist to environmental stresses, such as host defense mechanisms and pharmacological therapies.

Optimal decompositions for the K-functional for a couple of Banach lattices

Letf=gt+ht be the optimal decomposition for calculating the exact value of theK-functionalK(t, f;\(\bar X\)) of an elementf with respect to a couple\(\bar X\) =(X0 ,X1) of Banach lattices of measurable functions. It is shown that this decomposition has a rather simple form in many cases where one of the spacesX0 andX1 is eitherL∞ orL1. Many examples are given of couples of lattices\(\bar X\) for which |gt| increases monotonically a.e. with respect tot. It is shown that this property implies a sharpened estimate from above for the Brudnyi-KrugljakK-divisibility constant γ(\(\bar X\)) for the couple. But it is also shown that certain couples\(\bar X\) do not have this property. These also provide examples of couples of lattices for which γ(\(\bar X\)).

Convergence theorems and stability results for Lipschitz strongly pseudocontractive operators

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz strongly pseudocontractive operator. It is proved that under certain conditions the Ishikawa iterative method with errors converges strongly to the fixed point of T and this iteration procedure is stable with respect to T.

Stochastic differential game model of a common property fishery

The paper presents a stochastic differential game model of a common-property commercial fishery and determines a feedback Nash equilibrium of the game. Closed-form expressions for the value functions, the equilibrium harvesting strategies, and stationary distributions of the fish stock are derived. Sensitivity analyses with respect tot he model parameters are carried out. The paper also considers equilibrium outcomes under joint maximization and surplus maximization. In the latter case, an optimal market size (i.e., number of firms) is identified.

The Use of Blood Meal and Poultry Products as Partial Replacements for Fish Meal in Diets for Juvenile Palmetto Bass (Morone saxatilis×M. chrysops)

Feeding trials were conducted to determine the feasibility of using spray-dried blood meal (BM) or enzyme-hydrolyzed (EH) and low-ash (LA) poultry products to partially replace fish meal (FM) in diet formulations for palmetto bass. Pelleted diets were formulated with BM protein replacing 10, 25, or 50% of the FM protein and either EH or LA poultry products replacing approximately 25, 50, or 75% of the FM protein. All diets were formulated to contain 14kj GE energy/g and 35% crude protein. Fish fed a diet in which BM replaced 50% of the protein supplied by FM and significantly (P < 0.05) lower weight gain and feed efficiency compared to fish fed the control diet at the end of 6 to 12 weeks. Total body lipid was significantly higher form those fish receiving diets with 10 or 25% BM. However, there were not differences in total body moisture, protein, or ash. When either EH or LA protein replaced FM protein in the diet; there was not significant difference (P> 0.05) in growth among fish fed these diets as compared to those fed the control diet at either 6 or 11 weeks. There were no significant differences among fish fed different EH or LA diets with respect to total body protein or ash. However, there were differences among fish with respect tot moisture and lipid: as the percent of LA and EH increased in the diet, percent body moisture tended to increase at the expense of total body lipid. Data from these studies indicate that in appropriate amounts, BM and EH and LA poultry products can be substituted from FM in diets without significantly affecting growth and feed efficiency of juvenile palmetto bass.

Keldysh-Sedov formulas and differentiability with respect to the parameter of families of univalent functions inn-connected domains

We introduce families of functionsFj(w, t) mapping (n+1)-connected domains onto circular domains in thez-plane. Denote by Φj(z, t) the families of functions inverse toFj(w, t). Theorems 1–4 treat differentiability properties of these families with respect tot at a pointt=t0. We present formulas for the first derivative with respect tot. Corollaries of the theorems obtained are given. As a particular case, we deduce the theorem due to Kufarev for the disk and the theorem of Kufarev and Genina (Semukhina) for the annulus.

Two-gap elliptic solutions to integrable nonlinear equations

We study spectral surfaces associated with elliptic two-gap solutions to the nonlinear Schrodinger equation (NLS), the Korteweg-de Vries equation (KdV), and the sine-Gordon equation (SG). It is shown that elliptic solutions to the NLS and SG equations, as well as solutions to the KdV equation elliptic with respect tot, can be assigned to any hyperelliptic surface of genus 2 that forms a covering over an elliptic surface.

Mittelwerte von Hecke-Polynomen

In generalization of a classical result in number theory, we derive an estimate for the mean value of the Hecke polynomial $$S(t, \lambda ) = \sum {a(\mathfrak{a})} \lambda (\mathfrak{a})N\mathfrak{a}^{ - it} .$$ Here the sum runs over the integral ideals a of an algebraic number fieldK with normsNa≤X, and the mean value is defined via integration of |S(t, λ)|2 with respect tot∈[−T,T], and summation of the result over the Hecke Groessencharacters λ modulo some ideal f ofK having exponents <T. From this we derive an upper bound for the mean value of the fourth power of Hecke's zeta functions on the half-line Res=1/2.

On a class of exact locally conformal cosymlectic manifolds

An almost cosymplectic manifold M is a (2m + 1)‐dimensional oriented Riemannian manifold endowed with a 2‐form Ω of rank 2m, a 1‐form η such that Ωm Λ η ≠ 0 and a vector field ξ satisfying iξΩ = 0 and η(ξ) = 1. Particular cases were considered in [3] and [6].Let (M, g) be an odd dimensional oriented Riemannian manifold carrying a globally defined vector field T such that the Riemannian connection is parallel with respect to T. It is shown that in this case M is a hyperbolic space form endowed with an exact locally conformal cosymplectic structure. Moreover T defines an infinitesimal homothety of the connection forms and a relative infinitesimal conformal transformation of the curvature forms.The existence of a structure conformal vector field C on M is proved and their properties are investigated. In the last section, we study the geometry of the tangent bundle of an exact locally conformal cosymplectic manifold.

Application of the method of collective marks to someM/G/1 vacation models with exhaustive service

We use the Method of Collective Marks to analyze some time-dependent processes in theM/G/1 queue with single and multiple vacations. With the server state specified at a fixed timet>0, the Laplace transforms with respect tot of mixed transforms for the joint distribution of the number of departures by timet, the queue length, the virtual waiting time, the elapsed and remaining service/vacation times at timet are derived by means of probabilistic interpretations. The Laplace-Stieltjes transform of the virtual waiting time at timet is also given. Some well known results are special cases.

Residues of higher order and holomorphic vector fields

LetX 1 andX 2 be two holomorphic vector fields on a manifoldV with complex dimensionp. Assume that they have the same singular set ∑. For all $$C_I = (c_1 )^{i_1 } \cdot (c_2 )^{i_2 } \cdot \cdot \cdot (c_p )^{i_p } ,(i_1 + 2i_2 + \cdot \cdot \cdot + pi_p = p)$$ , it is known (after Chern-Bott) that each of the vector fields defines a “residual” characteristic classC 1(V,X 1)(resp.C 1(V,X 2)) inH 2p (V, V-∑), which is a lift of the usual characteristic classC 1 (V) of the tangent bundle. The differenceC 1 (V,X 2)-C 1 (V,X 1) belongs then to the image of ∂ in the exact sequence . In fact, there exists a canonical liftC 1 (V,X 1,X 2) of this difference inH 2p−1(V-∑): we will call itthe residual class of order 2 (associated toI, X 1 andX 2). This class is localized near the points whereX 1 andX 2 are colinear: we will explain this precisely in terms of Grothendieck residues. The formula that we obtain can be interpreted as a generalization of the purely algebraic identity, obtained from the general one as a byproduct: where (α 1, ⋯, αp) and (β 1,⋯, β p ) denote two families of non-zero complex numbers, such that all denominators in this formula do not vanish. (This identity corresponds in fact to the case whereX 1 andX 2 are non-degenerate at the same isolated singular point.) If theα i 's (1≤i≤p) depend now differentiably (resp. holomorphically) on a real (resp. complex) parametert then, denoting by the derivative with respect tot, and assuming all numbers lying in a denominator not to be 0, we can deduce from the above identity the following derivation formula:

The M/G/1 processor-sharing model: transient behavior

This paper deals with the M/G/1 model with processor-sharing service discipline. LetL*(t, x) denote the number of jobs present at timet whose attained service time is not greater thanx,x⩾0, andV0(t,z) the sojourn time of a tagged job placed in the system at timet and requiringz units of service. Explicit analytical expressions are obtained for the joint distribution ofL*(t, ·) andV0(t, ·) under various initial conditions in terms of the Laplace transform with respect tot. It is shown that for initial conditions of special kind (there is one job or none) the results can be expressed in a closed form.

Deformation resistance in oriented nylon 6

Initially spherulitic nylon 6 was textured into a quasi-single crystal form by plane-strain compression in deep channel-die, followed by cooling under pressure to room temperature. The resulting material, having orthotropic symmetry with quasi-single crystalline perfection, had a dual morphology in which the normals of the crystallographic (100) planes equipartition at ±20° with respect tot he constraint direction of the planne-strain deformation. This highly textured material, has relatively large dimensions in all directions, was used to study the elastic and plastic anisotropy of the actual constituent lamellar crystallites

Nutritional and antinutritional composition of vegetable and grain amaranth leaves

AbstractThe foliage of 61 accessionso f amaranthus comparising both the grain and vegetable types referable to 10 species were evaluated for carotenoid, protein, nitrate, odxalate and moisture contents (fresh weight). Carotenoid varied from 90 to 200 mg kg−1 in vegetable types and from 60 to 200 mg kg−1 in the leaves of grain types. Variation for leaf protein was found to be 14‐30, 15‐43 g kg−1; nitrate 1.8.‐8.8, 4.1‐9.2 g kg−1; oxalate 5.1‐19.2, 3‐16.5 g kg−1; and moisture 780‐860, 750‐840 g kg−1 in vegetable and grain types, respectively. Analysis of the amino acid composition of leaf protein of some high carotenoid lines revealed a well balanced composition with high lysine (40‐56 g kg−1). variation of all the five parameters (carotenoid, protein, nitrate, oxalate and moisture) with respect tot he leaf position in vegetable type (4‐ and 8‐week‐old plants) and with respect to age (‐ to 4‐month‐old plants) in grain types was also studied.

Quantum logics with the Radon-Nikodym property

Following the definition of S. Gudder and J. Zerbe, we say that a logicL has the Radon-Nikodym property (or, in short,L is an RN logic) if the following condition holds: Ifs, t are states onL ands is absolutely continuous with respect tot, then there is a central observablex such that\(s(a) = \int {_a x dt}\) for allaeL. We first consider general RN logics. We establish their basic properties and show that they are closed under the formation of epimorphisms and products. Then we take up the RN property for concrete logics. We first show that in many cases the concrete RN logics have to be ‘fully compatible’ (= Boolean σ-algebras). In contrast to that, we show that there are concrete RN logics with an arbitrary degree of noncompatibility. This extends the result of Navara and Ptak and answers in full the question posed by Gudder and Zerbe.

A generalization of the relative conditional expectatio—Further properties of Pitman'sT * and their applications to statistics

This paper is concerned with the mappingT * which is a generalization of the relative conditional expectation. It has been introduced by E.J.G. Pitman (1979,Some Basic Theory for Statistical Inference, Chapman and Hall). First we extend the definition of the mappingT * and describe its fundamental properties. Moreover, we establish inequalities for convex functions with respect toT *. The mappingT * is very useful in analysing quantities associated with the distribution of a statisticT. The application of the mappingT * to statistics is another interest of this paper.