Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

Ab initio study of MF2 (M=Mn, Fe, Co, Ni) rutile-type compounds using the periodic unrestricted Hartree-Fock approach

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the ground-state structural, electronic, and magnetic properties of the rutile-type compounds MF2 (M=Mn, Fe, Co, and Ni). All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the [001], [111], and [100] (or [010]) directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2 and CoF2 is also discussed.

Virus Infections in Early Childhood, Cow’s Milk Formula Exposure and Genetic Predisposition in the Development of Diabetes-Associated Autoimmunity

Varhaislapsuuden virusinfektioiden, lehmänmaitopohjaisen äidinmaitovastikeen ja geneettisen alttiuden merkitys diabetekseen liittyvän autoimmuniteetin kehittymisessä Tyypin 1 diabetes on autoimmuunisairaus, joka syntyy haiman insuliinia tuottavien beta-solujen tuhouduttua elimistön oman immuunipuolustusjärjestelmän hyökkäyksen seurauksena. Sekä perimän että ympäristötekijöiden arvellaan vaikuttavan tautiprosessiin, mutta taudin tarkkaa syntymekanismia ei tunneta. Tutkimuksen tarkoituksena oli selvittää varhaislapsuuden ympäristötekijöiden vaikutusta beta-soluautoimmuniteetin syntyyn, erityispaino tutkimuksessa oli ympäristötekijöiden yhteisvaikutuksessa sekä geneettisten riskitekijöiden ja ympäristötekijöiden vuorovaikutuksessa. Varhaislapsuudessa sairastettu sytomegalovirus- tai enterovirusinfektio ei lisännyt beta-soluautoimmuniteetin riskiä lapsilla, joilla on geneettisesti kohonnut riski sairastua tyypin 1 diabetekseen. Ennen puolen vuoden ikää sairastettu rotavirusinfektio lisäsi hieman tyypin 1 diabetekseen liittyvän autoimmuniteetin riskiä. Tarkemmassa analyysissa varhaislapsuuden enterovirusinfektio osoittautui kuitenkin autovasta-aineiden muodostumisen riskitekijäksi niiden lasten joukossa, jotka olivat saaneet lehmänmaitopohjaista äidinmaidon vastiketta ensimmäisten elinkuukausien aikana. Tämä löydös viittaa enterovirusinfektion ja lehmänmaitopohjaisen vastikkeen yhteisvaikutukseen tyypin 1 diabetekseen liittyvän autoimmuniteetin synnyssä. Löydösten mukaan PTPN22 geenin C1858T polymorfismi vaikuttaa CD4+ T solujen aktivaatioon ja proliferaatiovasteeseen, 1858T alleeliin liittyy alentunut T-soluresepto-rivälitteinen aktivaatio. 1858T alleelin kantajuuteen liittyy lisäksi lisääntynyt autovasta-aineiden ja kliinisen diabeteksen ilmaantuvuus. Tämä yhteys rajoittui yksilöihin, jotka olivat altistuneet lehmänmaitopohjaiselle vastikkeelle ennen kuuden kuukauden ikää. Tulosten mukaan sekä ympäristötekijöiden väliset yhteisvaikutukset että perimä vaikuttavat yksittäisen ympäristötekijän merkitykseen tyypin 1 diabetekseen liittyvän autoimmuniteetin synnyssä. Nämä yhteisvaikutukset ympäristötekijöiden kesken ja perimän ja ympäristötekijöiden välillä selittävät aiemmin julkaistujen tulosten ristiriittaisuutta tutkimuksissa, joissa on analysoitu vain yhden ympäristötekijän vaikutusta diabeteksen ilmaantuvuuteen.

Effect of metabolic syndrome and of its individual components on renal function of patients with type 2 diabetes mellitus

The objective of this study was to evaluate the effect of metabolic syndrome (MetS) and its individual components on the renal function of patients with type 2 diabetes mellitus (DM). A cross-sectional study was performed in 842 type 2 DM patients. A clinical and laboratory evaluation, including estimated glomerular filtration rate (eGFR) calculated by the modification of diet in renal disease formula, was performed. MetS was defined according to National Cholesterol Education Program - Adult Treatment Panel III criteria. Mean patient age was 57.9 ± 10.1 years and 313 (37.2%) patients were males. MetS was detected in 662 (78.6%) patients. A progressive reduction in eGFR was observed as the number of individual MetS components increased (one: 98.2 ± 30.8; two: 92.9 ± 28.1; three: 84.0 ± 25.1; four: 83.8 ± 28.5, and five: 79.0 ± 23.0; P < 0.001). MetS increased the risk for low eGFR (<60 mL·min-1·1.73 (m²)-1) 2.82-fold (95%CI = 1.55-5.12, P < 0.001). Hypertension (OR = 2.2, 95%CI = 1.39-3.49, P = 0.001) and hypertriglyceridemia (OR = 1.62, 95%CI = 1.19-2.20, P = 0.002) were the individual components with the strongest associations with low eGFR. In conclusion, there is an association between MetS and the reduction of eGFR in patients with type 2 DM, with hypertension and hypertriglyceridemia being the most important contributors in this sample. Interventional studies should be conducted to determine if treatment of MetS can prevent renal failure in type 2 DM patients.

La monnaie en droit : nature d'une abstraction outre fondée : essai dialectique et logique sur la dualité dans la catégoricité juridique et sur l'abstraction d'hérédité monétaire

"Thèse présentée à la Faculté des études supérieures en vue de l'obtention du grade de Docteur en droit (LL.D.)"

Scoliosis curve type classification from 3D trunk image

Adolescent idiopathic scoliosis (AIS) is a deformity of the spine manifested by asymmetry and deformities of the external surface of the trunk. Classification of scoliosis deformities according to curve type is used to plan management of scoliosis patients. Currently, scoliosis curve type is determined based on X-ray exam. However, cumulative exposure to X-rays radiation significantly increases the risk for certain cancer. In this paper, we propose a robust system that can classify the scoliosis curve type from non invasive acquisition of 3D trunk surface of the patients. The 3D image of the trunk is divided into patches and local geometric descriptors characterizing the surface of the back are computed from each patch and forming the features. We perform the reduction of the dimensionality by using Principal Component Analysis and 53 components were retained. In this work a multi-class classifier is built with Least-squares support vector machine (LS-SVM) which is a kernel classifier. For this study, a new kernel was designed in order to achieve a robust classifier in comparison with polynomial and Gaussian kernel. The proposed system was validated using data of 103 patients with different scoliosis curve types diagnosed and classified by an orthopedic surgeon from the X-ray images. The average rate of successful classification was 93.3% with a better rate of prediction for the major thoracic and lumbar/thoracolumbar types.

Selective N-monomethylation of aniline using Zn1-x CoxFe2O4( x=0, 0.2, 0.5, 0.8 and 1.0)type systems

A series of ferrites having the general formula Zn1-xCoxFe2O4 (x=0, 0.2, 0.5, 0.8 and 1.0)were prepared by soft chemical route. The materials were characterized by adopting various physico-chemical methods. The reaction of aniline with methanol was studied in a fixed-bed reactor system as a potential source for the production of various methyl anilines. It was observed that systems possessing low ‘ x’ values are highly selective and active for N-monoalkylation of aniline leading to N-methylaniline. Reaction parameters were properly varied to optimize the reaction conditions for obtaining N-methylaniline selectively and in better yield. Among the systems Zn0.8Co0.2Fe2O4 is remarkable due to its very high activity and excellent stability. Under the optimized conditions N-methylaniline selectivity exceeded 98%. Even at a methanol to aniline molar ratio of 2, the yield of N-methylaniline was nearly 50%, whereas its yield exceeded 71% at the molar ratio of 5. ZnFe2O4, though executed better conversion than Zn0.8Co0.2Fe2O4 in the initial period of the run, deactivates quickly as the reaction proceeds. The Lewis acidity of the catalysts is mainly responsible for the good performance. Cation distribution in the spinel lattice influences their acido-basic properties and, hence, these factors have been considered as helpful parameters to evaluate the activity of the systems.

Ab initio study of MF2 (M=Mn, Fe, Co, Ni) rutile-type compounds using the periodic unrestricted Hartree-Fock approach

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the ground-state structural, electronic, and magnetic properties of the rutile-type compounds MF2 (M=Mn, Fe, Co, and Ni). All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the [001], [111], and [100] (or [010]) directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2 and CoF2 is also discussed.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

A generic formula for the values at the boundary points of monic classical orthogonal polynomials

In a previous paper we have determined a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type σ(x)y"n(x)+τ(x)y'n(x)-λnyn(x)=0. In this paper, we give another such formula which enables us to present a generic formula for the values of monic classical orthogonal polynomials at their boundary points of definition.

Identifikation spezieller Funktionen, die durch Rodriguesformeln gegeben sind

Es ist allgemein bekannt, dass sich zwei gegebene Systeme spezieller Funktionen durch Angabe einer Rekursionsgleichung und entsprechend vieler Anfangswerte identifizieren lassen, denn computeralgebraisch betrachtet hat man damit eine Normalform vorliegen. Daher hat sich die interessante Forschungsfrage ergeben, Funktionensysteme zu identifizieren, die über ihre Rodriguesformel gegeben sind. Zieht man den in den 1990er Jahren gefundenen Zeilberger-Algorithmus für holonome Funktionenfamilien hinzu, kann die Rodriguesformel algorithmisch in eine Rekursionsgleichung überführt werden. Falls die Funktionenfamilie überdies hypergeometrisch ist, sogar laufzeiteffizient. Um den Zeilberger-Algorithmus überhaupt anwenden zu können, muss es gelingen, die Rodriguesformel in eine Summe umzuwandeln. Die vorliegende Arbeit beschreibt die Umwandlung einer Rodriguesformel in die genannte Normalform für den kontinuierlichen, den diskreten sowie den q-diskreten Fall vollständig. Das in Almkvist und Zeilberger (1990) angegebene Vorgehen im kontinuierlichen Fall, wo die in der Rodriguesformel auftauchende n-te Ableitung über die Cauchysche Integralformel in ein komplexes Integral überführt wird, zeigt sich im diskreten Fall nun dergestalt, dass die n-te Potenz des Vorwärtsdifferenzenoperators in eine Summenschreibweise überführt wird. Die Rekursionsgleichung aus dieser Summe zu generieren, ist dann mit dem diskreten Zeilberger-Algorithmus einfach. Im q-Fall wird dargestellt, wie Rekursionsgleichungen aus vier verschiedenen q-Rodriguesformeln gewonnen werden können, wobei zunächst die n-te Potenz der jeweiligen q-Operatoren in eine Summe überführt wird. Drei der vier Summenformeln waren bislang unbekannt. Sie wurden experimentell gefunden und per vollständiger Induktion bewiesen. Der q-Zeilberger-Algorithmus erzeugt anschließend aus diesen Summen die gewünschte Rekursionsgleichung. In der Praxis ist es sinnvoll, den schnellen Zeilberger-Algorithmus anzuwenden, der Rekursionsgleichungen für bestimmte Summen über hypergeometrische Terme ausgibt. Auf dieser Fassung des Algorithmus basierend wurden die Überlegungen in Maple realisiert. Es ist daher sinnvoll, dass alle hier aufgeführten Prozeduren, die aus kontinuierlichen, diskreten sowie q-diskreten Rodriguesformeln jeweils Rekursionsgleichungen erzeugen, an den hypergeometrischen Funktionenfamilien der klassischen orthogonalen Polynome, der klassischen diskreten orthogonalen Polynome und an der q-Hahn-Klasse des Askey-Wilson-Schemas vollständig getestet werden. Die Testergebnisse liegen tabellarisch vor. Ein bedeutendes Forschungsergebnis ist, dass mit der im q-Fall implementierten Prozedur zur Erzeugung einer Rekursionsgleichung aus der Rodriguesformel bewiesen werden konnte, dass die im Standardwerk von Koekoek/Lesky/Swarttouw(2010) angegebene Rodriguesformel der Stieltjes-Wigert-Polynome nicht korrekt ist. Die richtige Rodriguesformel wurde experimentell gefunden und mit den bereitgestellten Methoden bewiesen. Hervorzuheben bleibt, dass an Stelle von Rekursionsgleichungen analog Differential- bzw. Differenzengleichungen für die Identifikation erzeugt wurden. Wie gesagt gehört zu einer Normalform für eine holonome Funktionenfamilie die Angabe der Anfangswerte. Für den kontinuierlichen Fall wurden umfangreiche, in dieser Gestalt in der Literatur noch nie aufgeführte Anfangswertberechnungen vorgenommen. Im diskreten Fall musste für die Anfangswertberechnung zur Differenzengleichung der Petkovsek-van-Hoeij-Algorithmus hinzugezogen werden, um die hypergeometrischen Lösungen der resultierenden Rekursionsgleichungen zu bestimmen. Die Arbeit stellt zu Beginn den schnellen Zeilberger-Algorithmus in seiner kontinuierlichen, diskreten und q-diskreten Variante vor, der das Fundament für die weiteren Betrachtungen bildet. Dabei wird gebührend auf die Unterschiede zwischen q-Zeilberger-Algorithmus und diskretem Zeilberger-Algorithmus eingegangen. Bei der praktischen Umsetzung wird Bezug auf die in Maple umgesetzten Zeilberger-Implementationen aus Koepf(1998/2014) genommen. Die meisten der umgesetzten Prozeduren werden im Text dokumentiert. Somit wird ein vollständiges Paket an Algorithmen bereitgestellt, mit denen beispielsweise Formelsammlungen für hypergeometrische Funktionenfamilien überprüft werden können, deren Rodriguesformeln bekannt sind. Gleichzeitig kann in Zukunft für noch nicht erforschte hypergeometrische Funktionenklassen die beschreibende Rekursionsgleichung erzeugt werden, wenn die Rodriguesformel bekannt ist.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

Synthesis, reactivity, and X-ray crystal structure of some mixed-ligand oxovanadium(V) complexes: first report of binuclear oxovanadium(V) complexes containing 4,4 '-Bipyridine type bridge

Reaction of the tridentate ONO Schiff-base ligand 2-hydroxybenzoylhydrazone of 2-hydroxybenzoylhydrazine (H2L) with VO(acac)(2) in ethanol medium produces the oxoethoxovanadium(V) complex [VO(OEt)L] (A), which reacts with pyridine to form [VO(OEt)L center dot(py)] (1). Complex 1 is structurally characterized. It has a distorted octahedral O4N2 coordination environment around the V(V) acceptor center. Both complexes A and 1 in ethanol medium react with neutral monodentate Lewis bases 2-picoline, 3-picoline, 4-picoline, 4-amino pyridine, imidazole, and 4-methyl imidazole, all of which are stronger bases than pyridine, to produce dioxovanadium(V) complexes of general formula BH[VO2L]. Most of these dioxo complexes are structurally characterized, and the complex anion [VO2L](-) is found to possess a distorted square pyramidal structure. When a solution/suspension of a BH[VO2L] complex in an alcohol (ROH) is treated with HCl in the same alcohol, it is converted into the corresponding monooxoalkoxo complex [ O(OR)L], where R comes from the alcohol used as the reaction medium. Both complexes A and 1 produce the 4,4'-bipyridine-bridged binuclear complex [VO(OEt)L](2)(mu-4,4'-bipy) (2), which, to the best of our knowledge, represents the first report of a structurally characterized 4,4'-bipyridine-bridged oxovanadium(V) binuclear complex. Two similar binuclear oxovanadium(V) complexes 3 and 4 are also synthesized and characterized. All these binuclear complexes (2-4), on treatment with base B, produce the corresponding mononuclear dioxovanadium(V) complexes (5-10).

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.