Procedures to investigate injectivity of polynomial maps and to compute the inverse

In this paper a polynomial map from C ⁿ to C ^m is studied in order to investigate if it is injective out of a set of measure zero. We propose a procedure, based on truncated Gröbner basis computations, which when successful, allows to reduce the problem to an easier map, and so gives a speed-up of the general algorithms using Gröbner basis techniques. Moreover, for the special case of a polynomial map from C ⁿ to C ⁿ where the polynomials are at most quadratic, we propose two criteria for non-injectivity based on the structure of the Jacobian matrix and requiring only basic symbolic computations.     

Renal involvement in mushroom poisoning: The case of Orellanus syndrome

Although mushroom poisoning is a rare cause of acute renal injury, in some cases it may lead to the development of a severe and irreversible renal failure. Orellanus syndrome is the most important example of organic renal damage related to mushroom consumption. It is caused by the ingestion of orellanine, the main toxin of different types of Cortinarius mushrooms (Cortinarius speciosissimus, C. orellanus, C. orellanoides, etc.), and it is characterized by progressive clinical phases with a predominant kidney involvement, finally requiring renal replacement therapy in about 10% of cases. Renal damage is often late and associated with a histological picture of interstitial nephritis. Diagnosis is essentially clinical and no specific therapy has been shown to be effective in preventing and treating renal damage. Here, we describe the case of a patient with mixed wild mushroom poisoning, presenting the typical clinical signs and course of the Orellanus syndrome. This case offers us the opportunity to review the main clinical features of this severe and little‐known intoxication.     

Long binary narrow-sense BCH codes are normal

Let C be the binary narrow-sense BCH code of length n = (2 ^m − l)/h, where m is the order of 2 modulo n. Using characters of finite fields and a theorem of Weil, and results of Vladut-Skorobogatov and Lang-Weil we prove that the code C is normal in the non-primitive case h > 1 if 2^m ≥ 4(2th)^{4t + 2}, and in the primitive case h = 1 if m ≥ m ₀ where the constant m ₀ depends only on t.     

A rare case of Actinomyces skin and soft tissue infection in an end‐stage kidney disease patient with a review of the literature

End‐stage kidney disease (ESKD) patients are a commonly overlooked immunocompromised population that places them at risk for rare infections. We describe the case of a 78‐year‐old man with a history of ESKD managed with thrice weekly in‐center hemodialysis who had a prolonged episode of left elbow pain and drainage and was eventually found to have a skin and soft tissue infection from Actinomyces radingae. We review the bacteriology of Actinomyces spp. and the experiences of other providers who have treated actinomycosis in individuals with ESKD. The anatomic sites and demographics of these individuals are heterogeneous, but they all generally require a long antibiotic course with a beta‐lactam and portend to a good prognosis. High index of suspicion is needed to identify rare and atypical infections in the ESKD population.     

Cold Binary Atomic Collisions in a Light Field

The rate coefficients are calculated for trap loss due to excited state formation during s-wave collisions of two atoms in a light field in a cold atomic gas near conditions for formation of a Bose-Einstein condensate. Blue detuning from the allowed atomic resonance transition causes excitation of a replusive molecular potential, whereas red detuning causes excitation when the light is tuned near a bound vibrational energy level of an attractive molecular potential. In either case, when the light intensity is low and the detuning is large compared to the natural linewidth of the atomic transition, the rate coefficient for the collisional loss rate is proportional to a molecular Franck-Condon factor. A simple reflection approximation formula is derived which permits the rate coefficient to be given analytically in either case. The Franck-Condon factor is equal to |Ψ_g(R_C)²|/D_C, where Ψ_g(R_C) is the ground state scattering wavefunction at the Condon point R_C, where the quasimolecule is in resonance with the exciting light, and D_C is the slope difference between ground and excited potentials at R_C. The analytic reflection approximation formula, as well as a simple phase-amplitude formula for the intermediate range wavefunction, give excellent agreement with the results of numerical quantum mechanical calculations. The trap loss rates due to binary collisions are comparable to or exceed those due to atomic recoil heating for a wide range of detunings to the blue of atomic resonance and near the peaks of photoassociation resonances for the case of red detuning.     

Constraints on Weights in Binary Codes

 There are known constraints on the number of doubly-even and singly-even vectors in a linear even binary code C. These constraints give information about C∩C ^⊥. We find new constraints on weights in a binary linear code C which also contains odd weight vectors. This leads to information about the dimension and weights of C∩C ^⊥. Received: September 20, 1996     

干燥对2种栗属(Castanea)种子发芽率及水分状态的影响

目的 探究栗属种子的脱水敏感性，并研究干燥过程对胚轴水分状态的影响。方法 以采自河南的野生板栗和茅栗为实验材料，室温下在密闭容器中用硅胶快速干燥2种新鲜栗子，分别测定其干燥不同时间后水分含量和发芽率的变化并剥取胚轴。基于差式扫描量热技术（DSC），分析所取胚轴的热力学特征，并根据胚轴含水量和对应热焓值计算可冻结水与非冻结水的占比。结果 板栗干燥8d时，水分含量由49.51%降至32.97%，发芽率从78.33%降至8.5%；茅栗干燥4d时，水分含量由41.24%降至30.82%，发芽率从71.65%降至9.33%。种子水分含量低于30%时仅有少数种子发芽。DSC分析显示，实验过程中随着干燥时长的增加，胚轴的水分含量显著下降且与结晶/熔融阶段的起始温度、峰值温度和热焓值呈显著正相关。板栗的可冻结水分含量由89%降至7.9%，茅栗的可冻结水分含量由81%降至2.7%。结论 野生板栗和茅栗有极强的干燥敏感性，属典型顽拗性种子，其发芽率受水分含量高度影响，其胚轴的热物性参数和水分状态也与干燥程度密切相关。     

Contributions to the heat capacity of alpha (HCP) titanium from 200–1000 K

The heat capacity at constant pressure C _p of alpha (HCP) titanium from 200 to 1000 K has been analyzed for contributions from lattice vibrations and electron excitations. Experimental data in the literature have been used to obtain the heat capacity at constant volume C _V by the dilation correction. From C _V has been subtracted an harmonic lattice contribution C _VH given by the Debye heat capacity using a single Debye temperature and an electronic contribution C _VE . The difference C _V –(C _VH +C _VE ) is positive, and from about 600 to 1000 K it is real in the sense that it is larger than the experimental uncertainty in C _V . This difference is attributed to an anharmonic lattice vibration contribution C _VA . Two models for C _VE have been used. One, which includes electron-phonon enhancement, leads to a C _VA of about 15% of C _V at 1000 K. The other takes into account the shift in the density of states with temperature and leads to a C _VA of about 5% of C _V      

Bacterial adherence on UHMWPE with vitamin E: an in vitro study

Orthopaedic materials may improve its capacity to resist bacterial adherence, and subsequent infection. Our aim was to test the bacterial adherence to alpha-tocopherol (frequently named vitamin E, VE) doped or blended UHMWPE with S. aureus and S. epidermidis, compared to virgin material. Collection strains and clinical strains isolated from patients with orthopaedic infections were used, with the biofilm-developing ability as a covariable. While collection strains showed significantly less adherence to VE-UHMWPE, some clinical strains failed to confirm this effect, leading to the conclusion that VE doped or blended UHMWPE affects the adherence of some S. epidermidis and S. aureus strains, independently of the concentration in use, but the results showed important intraspecies differences and cannot be generalized.     

Conchoidal transform of two plane curves

The conchoid of a plane curve C is constructed using a fixed circle B in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves B and C in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in P ² × P ². We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve C we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.     

See the Unseen: Red-Emissive Carbon Dots for Visualizing the Nucleolar Structures in Two Model Animals and In Vivo Drug Toxicity

Nucleolus, which participates in many crucial cellular activities, is an ideal target for evaluating the state of a cell or an organism. Here, bright red-emissive carbon dots (termed CPCDs) with excitation-independent/polarity-dependent fluorescence emission are synthesized by a one-step hydrothermal reaction between congo red and p-phenylenediamine. The CPCDs can achieve wash-free, real-time, long-term, and high-quality nucleolus imaging in live cells, as well as in vivo imaging of two common model animals—zebrafish and Caenorhabditis elegans (C. elegans). Strikingly, CPCDs realize the nucleolus imaging of organs/flowing blood cells in zebrafish at a cellular level for the first time, and the superb nucleolus imaging of C. elegans suggests that the germ cells in the spermatheca probably have no intact nuclei. These previously unachieved imaging results of the cells/tissues/organs may guide the zebrafish-related studies and benefit the research of C. elegans development. More importantly, a novel strategy based on CPCDs for in vivo toxicity evaluation of materials/drugs (e.g., Ag⁺), which can visualize the otherwise unseen injuries in zebrafish, is developed. In conclusion, the CPCDs represent a robust tool for visualizing the structures and dynamic behaviors of live zebrafish and C. elegans, and may find important applications in cell biology and toxicology.     

Superconducting Transition of Two- and Three-Dimensional Networks in a Magnetic Field

We investigate the superconducting transition temperature T _C of two- and three-dimensional superconducting networks in a magnetic field. Making use of the de Gennes–Alexander equation, magnetic field dependence of the T _C and quantized fluxoid distributions are obtained. Especially, we calculate phase winding numbers of the superconducting order parameter around each closed path of the networks, and then deduce the fluxoid distributions. Two dimensional square lattice networks with edges have higher T _C than periodic square networks. For a three dimensional tetragonal network, T _C in the magnetic field perpendicular to the one of its face is much reduced in contrast to the case of a cubic network.     

A Cumulative Sum scheme for monitoring frequency and size of an event

This article proposes a Cumulative Sum (CUSUM) scheme, called the TC‐CUSUM scheme, for monitoring a negative or hazardous event. This scheme is developed using a two‐dimensional Markov model. It is able to check both the time interval (T) between occurrences of the event and the size (C) of each occurrence. For example, a traffic accident may be defined as an event, and the number of injured victims in each case is the event size. Our studies show that the TC‐CUSUM scheme is several times more effective than many existing charts for event monitoring, so that cost or loss incurred by an event can be reduced by using this scheme. Moreover, the TC‐CUSUM scheme performs more uniformly than other charts for detecting both T shift and C shift, as well as the joint shift in T and C. The improvement in the performance is achieved because of the use of the CUSUM feature and the simultaneous monitoring of T and C. The TC‐CUSUM scheme can be applied in manufacturing systems, and especially in non‐manufacturing sectors (e.g. supply chain management, health‐care industry, disaster management, and security control). Copyright © 2009 John Wiley & Sons, Ltd.     

Force and flow structures of a wing performing flapping motion at low Reynolds number

Summary Aerodynamic force and flow structures of a wing performing a simplified flapping motion that emulates the wing motion of small insects in normal hovering flight are studied, using the method of numerically solving the Navier-Stokes equations. For a typical case (wing rotation-axis is at 0.25 chord position and wing rotation is symmetrical with respect to stroke reversal), large peaks inC _L andC _D are produced near the end of a stroke by the wing-rotation, but the wing-rotation also generates a vortical structure which induces strong downwash velocity, reducing the lift production in the early part of the following stroke; averaging over one flapping cycle,C _L is 28% larger than the steady-state value and is about that needed to support the weight of a small insect. The timing of the wing-rotation at stroke reversal can change the size of the peaks inC _L andC _D and their averages; e.g. in the case of shifting the wing-rotation forward in time by 7.5% of a stroke period, the averageC _L becomes 63% larger than the steady-state value, which is larger than that needed for weight supporting (and might provide extra force for control or maneuvers). When the rotation-axis is moved rearward to the middlechord position, the lift and drag peaks due to the wing-rotation become smaller, and in this case, the wing-rotation generates a vortical structure that tends to prevent the relative motion between positive and negative vorticities, also reducing the lift production in the early part of the following stroke, resulting in a smaller averageC _L .     

Statistical Mechanical Study of Thermodynamic Properties of a Family of Fullerites from C36 to C96 in the Equilibrium with Their Vapors

Abstract

The temperature dependence of saturated vapor pressure of fullerites C₃₆–C₉₆ and their thermodynamic properties along with the sublimation curves up to the spinodal are calculated. The saturated vapor pressures along all the range of temperatures are approximated by logP _sat = A ? (B/T) ? CT. The coefficient A practically does not depend on the number of atoms in the molecule (varying only by 2.2%), B increases noticeably while C decreases from the C₃₆ to the C₉₆, both of them by approximately two. The isothermal bulk modulus B _T and the shear modulus C₄₄ vanish at the spinodal points.     

The onset of steady Marangoni convection in a spherical geometry

In this paper we use a combination of analytical and numerical techniques to analyse the onset of steady Marangoni convection in a spherical shell of fluid with an outer free surface surrounding a rigid sphere. In so doing we correct the formulation of the problem and the results presented by Cloot & Lebon (Microgravity sci. technol. 3 (1) 1990: 44–46). We find that if the free surface of the layer is non-deformable then the layer is always stable when heated from the outside and is unstable when heated from the inside if the magnitude of the (positive) non-dimensional Marangoni number is sufficiently large. If the free surface of the layer is deformable then the layer is always unstable when heated from the inside. It is stable when heated from the outside if C _r < r ₂/4, but if C _r > r ₂/4 then it is unstable if the magnitude of the (negative) Marangoni number is sufficiently large, where C _r is the non-dimensional Crispation number and r ₂ the non-dimensionalradius of the undisturbed outer free surface of the fluid.     

Uremic pleuritis in chronic hemodialysis patients

Chronic hemodialysis (HD) patients are predisposed to several complications associated with pleural effusion. In addition, uremia can directly cause pleuritis. However, there are inadequate data about pathogenesis and natural course of uremic pleuritis. In this study, 76 chronic HD patients with pleural effusion admitted to the Respiratory Center of Masih Daneshvari Hospital, in Tehran, Iran between June 2005 and May 2011 were evaluated to figure out the etiology of their pleural disease. Among these patients, patients with uremic pleuritis were identified and studied. The rate of uremic pleuritis was 23.7%. Other frequent etiologies of pleural effusion were parapneumonic effusion (23.7%), cardiac failure (19.7%), tuberculosis (6.6%), volume overload, malignancy, and unknown. In patients with uremic pleuritis, dyspnea was the most common symptom, followed by cough, weight loss, anorexia, chest pain, and fever. Compared to patients with parapneumonic effusion, patients with uremic effusion had a significantly higher rate of dyspnea and lower rate of cough and fever. Pleural fluid analysis showed that these patients had a significantly lower pleural to serum lactic dehydrogenase ratio, total pleural leukocytes, and polymorphonuclear count compared to patients with parapneumonic effusion. Improvement was achieved in 94.1% of patients with uremic pleuritis by continuation of HD, chest tube insertion or pleural decortication; an outcome better than the previous reports. Despite the association with an exudative effusion, inflammatory pleural reactions in patients with uremic pleuritis may not be as severe as infection‐induced effusions. Owing to the advancement in HD technology and other interventions, outcome of uremic pleuritis may be improved.     

Efficient and accurate four-node quadrilateral C0 plate bending element based on assumed strain fields

Based on the assumed element strain fields and the interrelated displacement-rotation interpolations, a four-node (12 dof) quadrilateral C⁰ finite element, designated as QCCP-2, for the analysis of thick/thin plates is developed in this paper. The four-node C⁰ plate element presented here possesses a linear bending strain field, and the element stiffness matrices are given explicitly. Therefore, the present four-node C⁰ plate element is more efficient and accurate than the existing four-node C⁰ plate elements where the constant strain stiffness matrices are obtained by numerical integration. By the use of the interrelated displacement-rotation interpolations, QCCP-2 is capable of automatically satisfying the Kirchhoff assumption for the case of thin plates. Consequently, QCCP-2 is not only free of shear locking, but also free from the numerical ill-conditioning. Furthermore, QCCP-2 passes the patch test of thin plates. The four-node quadrilateral C⁰ elements presented here can automatically reduce to the corresponding three-node triangular elements. Several numerical examples are given to demonstrate the efficiency and accuracy of the C⁰ plate bending element QCCP-2.     

Bounds on the minimum distance of the duals of extended BCH codes over\mathbb{F}_p

LetC be an extended cyclic code of lengthp ^m over . The border ofC is the set of minimal elements (according to a partial order on [0,p ^m –1]) of the complement of the defining-set ofC. We show that an affine-invariant code whose border consists of only one cyclotomic coset is the dual of an extended BCH code if, and only if, this border is the cyclotomic coset, sayF(t, i), ofp ^t –1–i, with 1 t m and 0 i < p–1. We then study such privileged codes. We first make precize which duals of extendedBCH codes they are. Next, we show that Weil's bound in this context gives an explicit formula; that is, the couple (t, i) fully determines the value of the Weil bound for the code with borderF(t, i). In the case where this value is negative, we use the Roos method to bound the minimum distance, greatly improving the BCH bound.     

Noncovalent complexes of Ih−C80 fullerene with phthalocyanines

The noncovalent interactions of I_h?C₈₀ fullerene with free-base and 3d transition M(II) phthalocyanines (where M = Mn, Fe, Co, Ni, Cu, Zn) were studied at the PBE-D/DNP level of density functional theory. The optimized complex geometries, formation energies and electronic parameters were analyzed and compared to those reported previously for similar dyads with C₆₀. In the complexes with I_h?C₈₀, the central metal atom (as well as one H atom of H₂Pc) is always coordinated to a C_6:6:6 atom of C₈₀ cage, exhibiting only one general interaction pattern. The shortest M^…C_C80 and N^…C_C80 distances are notably longer than in dyads with C_60, and the distortion of Pc macrocycle is less significant. In none of C₈₀-based dyads the formation of new coordination bonds by metal atoms was observed. The bonding strength for Pc–C₈₀ dyads varies approximately to the same degree of 20 kcal/mol as for their Pc–C₆₀ analogues, however negative formation energies for Pc–C₈₀ dyads are on average by 5–6 kcal/mol lower than for their C₆₀ analogues. While in closed-shell Pc–fullerene systems HOMO is usually found totally on Pc molecule, in the case of C₈₀-based dyads only a minor HOMO fraction can be detected for some dyads on Pc, with the major one always distributed over fullerene cage. As a result, the calculated HOMO-LUMO gap energies turn to be very low, around 0.1 eV. Analysis of spin density plots revealed that H₂Pc+C₈₀, NiPc+C₈₀ and ZnPc+C₈₀ dyads behave as closed-shell systems, like similar noncovalent complexes of Pcs with C₆₀.