The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Orientation to light of juvenile and adult forms of melanic and albino populations of Biomphalaria glabrata (Say, 1818)

The process of light orientation by the snail Biomphalaria glabrata was studied using the selection technique in a Y-shaped aquarium under vertical or horizontal lighting schemes. Snail behavior was measured on the basis of distance (cm) covered per hour, direction of locomotion, and localization of the animal in the aquarium. A comparison was made of the action of the light stimulus on young and adult animals of albino populations from Santa Luzia (State of Minas Gerais, Brazil) and of a melanic population from Touros (State of Rio Grande do Norte) studied in groups and separately. All groups studied were attracted to light. Analysis of the data suggests the exitence of two orientation mechanisms with respect to light in these animals, i.e. high photo-orthokinesia and positive phototaxis, which influence their motion in the environment. This evidence permitted us to discuss features of the distribution dynamics of these mollusks in the environment and their relationship with the larval phases of Schistosoma mansoni, for which they act as intermediated hosts.

Synthesis and characterization of a new class of anti-angiogenic agents based on ruthenium clusters.

New triruthenium-carbonyl clusters derivatized with glucose-modified bicyclophosphite ligands have been synthesized. These compounds were found to have cytostatic and cytotoxic activity and depending on the number of bicyclophosphite ligands, and could be tuned for either anti-cancer or specific anti-angiogenic activity. While some compounds had a broad cellular toxicity profile in several cell types others showed endothelial cell specific dose-dependent anti-proliferative and anti-migratory efficacy. A profound inhibition of angiogenesis was also observed in the in vivo chicken chorioallantoic membrane (CAM) model, and consequently, these new compounds have considerable potential in drug design, e.g. for the treatment of cancer.

Parametrization of spectral surfaces of a class of periodic 5-diagonal matrices

The main result of this work is a parametric description of the spectral surfaces of a class of periodic 5-diagonal matrices, related to the strong moment problem. This class is a self-adjoint twin of the class of CMV matrices. Jointly they form the simplest possible classes of 5-diagonal matrices.

Capacity to within one bit of a class of Gaussian multicast channels with interference

This paper studies the fundamental operational limits of a class of Gaussian multicast channels with an interference setting. In particular, the paper considers two base stations multicasting separate messages to distinct sets of users. In the presence of channel state information at the transmitters and at the respective receivers, the capacity region of the Gaussian multicast channel with interference is characterized to within one bit. At the crux of this result is an extension to the multicast channel with interference of the Han-Kobayashi or the Chong-Motani-Garg achievable region for the interference channel.

A general class of adaptative strategies

We exhibit and characterize an entire class of simple adaptive strategies,in the repeated play of a game, having the Hannan-consistency property: In the long-run, the player is guaranteed an average payoff as large as the best-reply payoff to the empirical distribution of play of the otherplayers; i.e., there is no "regret." Smooth fictitious play (Fudenberg and Levine [1995]) and regret-matching (Hart and Mas-Colell [1998]) areparticular cases. The motivation and application of this work come from the study of procedures whose empirical distribution of play is, in thelong-run, (almost) a correlated equilibrium. The basic tool for the analysis is a generalization of Blackwell's [1956a] approachability strategy for games with vector payoffs.

EFFECTS OF PLANTING DATE AND SPATIAL ARRANGEMENT ON COMMON BEAN (Phaseolus vulgaris) YIELD UNDER WEED-FREE AND WEEDY CONDITIONS

ABSTRACTTo evaluate the effect of planting date and spatial pattern on common bean yield under weed-free and weed-infested conditions, an experiment was conducted in Kelachay, Northern Iran, in 2013. The experimental design was a randomized complete block in a factorial arrangement with three replicates. Factors were planting date (10 August and 20 August), spatial pattern (square and rectangular planting pattern, with a planting distance of 30 x 30 cm and 45 x 20 cm, respectively), and weed management regime (weed-free and weedy conditions, weeded and not weeded throughout the growing season, respectively). Results showed that the main effect of planting date was significant only for pod number per plant and seed number per pod. At the same time, pod number per plant, seed number per pod, pod length, and grain yield were influenced significantly by spatial pattern. Results of ANOVA have also indicated that all traits, except pod length, were influenced significantly by weed-management regimes. Moreover, effect of planting date and spatial pattern were nonsignificant for weed dry weight. Mean comparison has expressed a significant increment in seed yield for square planting arrangement (1,055 kg ha-1) over rectangular (971 kg ha-1). Weeding has also presented an overall 12% and 8% improvement in grain and pod yield over control (weedy check), respectively. Based on the results of this study, weed control, as well as square planting pattern, are recommended for obtaining the highest seed yield in common bean.

Viral membrane fusion: is glycoprotein G of rhabdoviruses a representative of a new class of viral fusion proteins?

Enveloped viruses always gain entry into the cytoplasm by fusion of their lipid envelope with a cell membrane. Some enveloped viruses fuse directly with the host cell plasma membrane after virus binding to the cell receptor. Other enveloped viruses enter the cells by the endocytic pathway, and fusion depends on the acidification of the endosomal compartment. In both cases, virus-induced membrane fusion is triggered by conformational changes in viral envelope glycoproteins. Two different classes of viral fusion proteins have been described on the basis of their molecular architecture. Several structural data permitted the elucidation of the mechanisms of membrane fusion mediated by class I and class II fusion proteins. In this article, we review a number of results obtained by our laboratory and by others that suggest that the mechanisms involved in rhabdovirus fusion are different from those used by the two well-studied classes of viral glycoproteins. We focus our discussion on the electrostatic nature of virus binding and interaction with membranes, especially through phosphatidylserine, and on the reversibility of the conformational changes of the rhabdovirus glycoprotein involved in fusion. Taken together, these data suggest the existence of a third class of fusion proteins and support the idea that new insights should emerge from studies of membrane fusion mediated by the G protein of rhabdoviruses. In particular, the elucidation of the three-dimensional structure of the G protein or even of the fusion peptide at different pH's might provide valuable information for understanding the fusion mechanism of this new class of fusion proteins.

Oligo(p-Phenylenevinylene) Derived Organogels: A Novel Class of Functional Supramolecular Materials

The main objective of the present study is to have a detailed investigation on the gelation properties, morphology and optical properties of small π-conjugated oligomers. For this purpose we have chosen oligo(p-phenylenevinylene)s (OPVs), a class of molecules which have received considerable attention due to their unique optical and electronic properties. Though a large number of reports are available in the literature on the self-assembly properties of tailor made OPVs, none of them pertain to the design of nanostructures based on organogels. In view of this, we aimed at the creation of functional chromophoric assemblies of π-conjugated OPVs through the formation of organogels, with the objective of crafting nanoscopic assemblies of different size and shape thereby modulating their optical and electronic properties.In order to fulfill the above objectives, the design and synthesis of a variety of OPVs with appropriate structural variations were planned. The design principle involves the derivatization of OPVs with weak H-bonding hydroxymethyl end groups and with long aliphatic hydrocarbon side chains. The noncovalent interactions in these molecules were expected to lead the formation of supramolecular assembly and gels in hydrocarbon solvents. In such an event, detailed study of gelation and extensive analysis of the morphology of the gel structures were planned using advanced microscopic techniques. Since OPVs are strongly fluorescent molecules, gelation is expected to perturb the optical properties. Therefore, detailed study on the gelation induced optical properties as a way to probe the nature and stability of the selfassembly was planned. Apart from this, the potential use of the modulation of the optical properties for the purpose of light harvesting was aimed. The approach to this problem was to entrap an appropriate energy trap to the OPV gel matrix which may lead to the efficient energy transfer from the OPV gel based donor to the entrapped acceptor. The final question that we wanted to address in this investigation was the creation of helical nanostructures through proper modification of the OPV backbone With chiral handles.The present thesis is a detailed and systematic approach to the realization of the above objectives which are presented in different chapters of the thesis.

A New Class of Nonionic Photosensitive Surfactants: Some Insights Concerning Conformations

We report on a new class of nonionic, photosensitive surfactants consisting of a polar di(ethylene oxide) head group attached to an alkyl spacer of between two and eight methylene groups, coupled through an ether linkage to an azobenzene moiety. Structural changes associated with the interconversion of the azobenzene group between its cis and trans forms as mediated by the wavelength of an irradiating light source cause changes in the surface tension and self-assembly properties. Differences in saturated surface tensions (surface tension at concentrations above the CMC) were as high as 14.4 mN/m under radiation of different wavelengths. The qualitative behavior of the surfactants changed as the spacer length changed, attributed to the different orientations adopted by the different surfactants depending on their isomerization states, as revealed by neutron reflection studies. The self-assembly of these photosensitive surfactants has been investigated by light scattering, small angle neutron scattering, and cryo-TEM under different illuminations. The significant change in the self-assembly in response to different illumination conditions was attributed to the sign change in Gaussian rigidity, which originated from the azobenzene photoisomerization.

Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

A high frequency boundary element method for scattering by a class of nonconvex obstacles

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

Exact vortex solutions in a CP(N) Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CP(N) which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP(1). We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x(1) + i x(2)) and (x(3) + x(0)) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.

A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.