Some Completely Monotonic Properties for the (p, g)-Gamma Function

MSC 2010: 33B15, 26A51, 26A48

Series representations of the remainders in the expansions for certain functions with applications

We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1)2/(et+1) , sech t and coth t and establish simple bounds for these remainders when t>0t>0 . Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.

KINEMATIC SYNTHESIS AND ANALYSIS OF THE RACK AND PINION MULTIPURPOSE MECHANISM

The general procedure for synthesizing the rack and pinion mechanism up to seven precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for three precision conditions of path generation, two positions of function generation, and a velocity condition at one of the precision points. This mechanism has a number of advantages over conventional four bar mechanisms. First, since the rack is always tangent to the pinion, the transmission angle is always 90 deg minus the pressure angle of the rack. Second, with both translation and rotation of the rock occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide variety of motion and nonmonotonic functions for a full range of motion as well as nonlinear amplified motions. In this work the mechanism is made to satisfy a number of amplified motions. In this work the mechanism is made to satisfy a number of practical design requirements such as completely rotatable input crank and others. By including the velocity specification, the designer has considerably more control of the output motion. The method of solution developed in this work uses the complex number method of mechanism synthesis. A numerical example is included

Kinematic Synthesis and Analysis of the Rack and Pinion Multi-Purpose Mechanism

The general procedure for synthesizing the rack and pinion mechanism up to seven precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for three precision conditions of path generation, two positions of function generation, and a velocity condition at one of the precision points. This mechanism has a number of advantages over conventional four bar mechanisms. First, since the rack is always tangent to the pinion, the transmission angle is always 90 deg minus the pressure angle of the rack. Second, with both translation and rotation of the rack occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide variety of motion and nonmonotonic functions for a full range of motion as well as nonlinear amplified motions. In this work the mechanism is made to satisfy a number of practical design requirements such as completely rotatable input crank and others. By including the velocity specification, the designer has considerably more control of the output motion. The method of solution developed in this work uses the complex number method of mechanism synthesis. A numerical example is included.

The ADP Ribosylation Factor-Nucleotide Exchange Factors Gea1p and Gea2p Have Overlapping, but Not Redundant Functions in Retrograde Transport from the Golgi to the Endoplasmic Reticulum

The activation of the small ras-like GTPase Arf1p requires the action of guanine nucleotide exchange factors. Four Arf1p guanine nucleotide exchange factors have been identified in yeast: Sec7p, Syt1p, Gea1p, and its homologue Gea2p. We identified GEA2 as a multicopy suppressor of a sec21-3 temperature-sensitive mutant. SEC21 encodes the γ-subunit of coatomer, a heptameric protein complex that together with Arf1p forms the COPI coat. GEA1 and GEA2 have at least partially overlapping functions, because deletion of either gene results in no obvious phenotype, whereas the double null mutant is inviable. Conditional mutants defective in both GEA1 and GEA2 accumulate endoplasmic reticulum and Golgi membranes under restrictive conditions. The two genes do not serve completely overlapping functions because a Δgea1 Δarf1 mutant is not more sickly than a Δarf1 strain, whereas Δgea2 Δarf1 is inviable. Biochemical experiments revealed similar distributions and activities for the two proteins. Gea1p and Gea2p exist both in membrane-bound and in soluble forms. The membrane-bound forms, at least one of which, Gea2p, can be visualized on Golgi structures, are both required for vesicle budding and protein transport from the Golgi to the endoplasmic reticulum. In contrast, Sec7p, which is required for protein transport within the Golgi, is not required for retrograde protein trafficking.

Elemental composition of solar energetic particles

The Low Energy Telescopes on the Voyager spacecraft are used to measure the elemental composition (2 ≤ Z ≤ 28) and energy spectra (5 to 15 MeV /nucleon) of solar energetic particles (SEPs) in seven large flare events. Four flare events are selected which have SEP abundance ratios approximately independent of energy/nucleon. The abundances for these events are compared from flare to flare and are compared to solar abundances from other sources: spectroscopy of the photosphere and corona, and solar wind measurements.

The selected SEP composition results may be described by an average composition plus a systematic flare-to-flare deviation about the average. For each of the four events, the ratios of the SEP abundances to the four-flare average SEP abundances are approximately monotonic functions of nuclear charge Z in the range 6 ≤ Z ≤ 28. An exception to this Z-dependent trend occurs for He, whose abundance relative to Si is nearly the same in all four events.

The four-flare average SEP composition is significantly different from the solar composition determined by photospheric spectroscopy: The elements C, N and O are depleted in SEPs by a factor of about five relative to the elements Na, Mg, Al, Si, Ca, Cr, Fe and Ni. For some elemental abundance ratios (e.g. Mg/O), the difference between SEP and photospheric results is persistent from flare to flare and is apparently not due to a systematic difference in SEP energy/nucleon spectra between the elements, nor to propagation effects which would result in a time-dependent abundance ratio in individual flare events.

The four-flare average SEP composition is in agreement with solar wind abundance results and with a number of recent coronal abundance measurements. The evidence for a common depletion of oxygen in SEPs, the corona and the solar wind relative to the photosphere suggests that the SEPs originate in the corona and that both the SEPs and solar wind sample a coronal composition which is significantly and persistently different from that of the photosphere.

A Lower-Bound Result on the Power of a Genetic Algorithm

This paper presents a lower-bound result on the computational power of a genetic algorithm in the context of combinatorial optimization. We describe a new genetic algorithm, the merged genetic algorithm, and prove that for the class of monotonic functions, the algorithm finds the optimal solution, and does so with an exponential convergence rate. The analysis pertains to the ideal behavior of the algorithm where the main task reduces to showing convergence of probability distributions over the search space of combinatorial structures to the optimal one. We take exponential convergence to be indicative of efficient solvability for the sample-bounded algorithm, although a sampling theory is needed to better relate the limit behavior to actual behavior. The paper concludes with a discussion of some immediate problems that lie ahead.

Effects of mandibular fixed implant-supported prostheses on masticatory and swallowing functions in completely edentulous elderly individuals

Purpose: To evaluate the effect of oral rehabilitation with immediately loaded fixed implant-supported mandibular prostheses on chewing and swallowing in elderly individuals. Materials and Methods: Fifteen completely edentulous patients aged more than 60 years (10 women and rive men), wearing removable dentures in both arches, had a mandibular denture replaced by an implant-supported prosthesis. All individuals were evaluated before surgery and again 3, 6, and 18 months later with regard to mastication and swallowing conditions. Examinations entailed an interview, evaluation of tactile sensitivity of the face, and observation of food intake, masticatory type, formations of bolus, and pain during mastication. The swallowing evaluation comprised observation of clinical signs related to the oral and pharyngeal stages of swallowing, as well as the presence of oral residue. The findings of different evaluations before and 3, 6, and 18 months after the surgical-prosthetic procedure were statistically compared by analysis of variance for repeated measurements at a significance level of 5%. Results: The questionnaire revealed a reduction in complaints of masticatory and swallowing disturbances, a decreased need for liquid ingestion, and reduced choking and coughing. Clinical evaluations showed improved oral function and bolus propulsion for both solid and paste-consistency foods; pain during mastication was also resolved. Conclusion: Treatment with mandibular implant-supported dentures had positive effects on the clinical aspects of mastication and swallowing in elderly individuals.

Learning Optimal Discriminant Functions through a Cooperative Game of Automata

The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. The problem of learning such optimal discriminant functions is considered for the class of problems where the statistical properties of the pattern classes are completely unknown. The problem is posed as a game with common payoff played by a team of mutually cooperating learning automata. This essentially results in a probabilistic search through the space of classifiers. The approach is inherently capable of learning discriminant functions that are nonlinear in their parameters also. A learning algorithm is presented for the team and convergence is established. It is proved that the team can obtain the optimal classifier to an arbitrary approximation. Simulation results with a few examples are presented where the team learns the optimal classifier.

Neuromagnetic studies on cortical somatosensory functions in infants and children : Normal development and effect of early brain lesions

Until recently, objective investigation of the functional development of the human brain in vivo was challenged by the lack of noninvasive research methods. Consequently, fairly little is known about cortical processing of sensory information even in healthy infants and children. Furthermore, mechanisms by which early brain insults affect brain development and function are poorly understood. In this thesis, we used magnetoencephalography (MEG) to investigate development of cortical somatosensory functions in healthy infants, very premature infants at risk for neurological disorders, and adolescents with hemiplegic cerebral palsy (CP). In newborns, stimulation of the hand activated both the contralateral primary (SIc) and secondary somatosensory cortices (SIIc). The activation patterns differed from those of adults, however. Some of the earliest SIc responses, constantly present in adults, were completely lacking in newborns and the effect of sleep stage on SIIc responses differed. These discrepancies between newborns and adults reflect the still developmental stage of the newborns’ somatosensory system. Its further maturation was demonstrated by a systematic transformation of the SIc response pattern with age. The main early adult­like components were present by age two. In very preterm infants, at term age, the SIc and SIIc were activated at similar latencies as in healthy fullterm newborns, but the SIc activity was weaker in the preterm group. The SIIc response was absent in four out of the six infants with brain lesions of the underlying hemisphere. Determining the prognostic value of this finding remains a subject for future studies, however. In the CP adolescents with pure subcortical lesions, contrasting their unilateral symptoms, the SIc responses of both hemispheres differed from those of controls: For example the distance between SIc representation areas for digits II and V was shorter bilaterally. In four of the five CP patients with cortico­subcortical brain lesions, no normal early SIc responses were evoked by stimulation of the palsied hand. The varying differences in neuronal functions, underlying the common clinical symptoms, call for investigation of more precisely designed rehabilitation strategies resting on knowledge about individual functional alterations in the sensorimotor networks.

Derivation and consistency of the partial functions of the ternary system involving interaction coefficients

The logarithm of activity coefficients of the components of the ternary system is derived based on the Maclaurin infinite series, which is expressed in terms of the integral property of the system and subjected to appropriate boundary conditions. The derivation of the functions involves extensive summation of various infinite series pertaining to the first-order interaction coefficients that have been shown completely to remove any truncational error. Since the conventional equations involving interaction coefficients are internally inconsistent, a consistent form of the partial functions is developed in the article using the technique just described. The thermodynamic consistency of the functions based on the Maxwell and the Gibbs-Duhem relations has been established. The derived values of the logarithmic activity coefficients of the components have been found to be in agreement with the thermodynamic data of the Fe-Cr-Ni system at 1873 K and have been found to be independent of the compositional paths.

The advection-condensation model and water-vapour probability density functions

The statistically steady humidity distribution resulting from an interaction of advection, modelled as an uncorrelated random walk of moist parcels on an isentropic surface, and a vapour sink, modelled as immediate condensation whenever the specific humidity exceeds a specified saturation humidity, is explored with theory and simulation. A source supplies moisture at the deep-tropical southern boundary of the domain and the saturation humidity is specified as a monotonically decreasing function of distance from the boundary. The boundary source balances the interior condensation sink, so that a stationary spatially inhomogeneous humidity distribution emerges. An exact solution of the Fokker-Planck equation delivers a simple expression for the resulting probability density function (PDF) of the wate-rvapour field and also the relative humidity. This solution agrees completely with a numerical simulation of the process, and the humidity PDF exhibits several features of interest, such as bimodality close to the source and unimodality further from the source. The PDFs of specific and relative humidity are broad and non-Gaussian. The domain-averaged relative humidity PDF is bimodal with distinct moist and dry peaks, a feature which we show agrees with middleworld isentropic PDFs derived from the ERA interim dataset. Copyright (C) 2011 Royal Meteorological Society

Dimethyl sulfoxide induced structural transformations and non-monotonic concentration dependence of conformational fluctuation around active site of lysozyme

Experimental studies have observed significant changes in both structure and function of lysozyme (and other proteins) on addition of a small amount of dimethyl sulfoxide (DMSO) in aqueous solution. Our atomistic molecular dynamic simulations of lysozyme in water-DMSO reveal the following sequence of changes on increasing DMSO concentration. (i) At the initial stage (around 5% DMSO concentration) protein's conformational flexibility gets markedly suppressed. From study of radial distribution functions, we attribute this to the preferential solvation of exposed protein hydrophobic residues by the methyl groups of DMSO. (ii) In the next stage (10-15% DMSO concentration range), lysozome partially unfolds accompanied by an increase both in fluctuation and in exposed protein surface area. (iii) Between 15-20% concentration ranges, both conformational fluctuation and solvent accessible protein surface area suddenly decrease again indicating the formation of an intermediate collapse state. These results are in good agreement with near-UV circular dichroism (CD) and fluorescence studies. We explain this apparently surprising behavior in terms of a structural transformation which involves clustering among the methyl groups of DMSO. (iv) Beyond 20% concentration of DMSO, the protein starts its final sojourn towards the unfolding state with further increase in conformational fluctuation and loss in native contacts. Most importantly, analysis of contact map and fluctuation near the active site reveal that both partial unfolding and conformational fluctuations are centered mostly on the hydrophobic core of active site of lysozyme. Our results could offer a general explanation and universal picture of the anomalous behavior of protein structure-function observed in the presence of cosolvents (DMSO, ethanol, tertiary butyl alcohol, dioxane) at their low concentrations. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3694268]

The HORMA domain: an evolutionarily conserved domain discovered in chromatin-associated proteins, has unanticipated diverse functions

The HORMA domain (for Hop1p, Rev7p and MAD2) was discovered in three chromatin-associated proteins in the budding yeast Saccharomyces cerevisiae. This domain has also been found in proteins with similar functions in organisms including plants, animals and nematodes. The HORMA domain containing proteins are thought to function as adaptors for meiotic checkpoint protein signaling and in the regulation of meiotic recombination. Surprisingly, new work has disclosed completely unanticipated and diverse functions for the HORMA domain containing proteins. A. M. Villeneuve and colleagues (Schvarzstein et al., 2013) show that meiosis-specific HORMA domain containing proteins plays a vital role in preventing centriole disengagement during Caenorhabditis elegans spermatocyte meiosis. Another recent study reveals that S. cerevisiae Atg13 HORMA domain acts as a phosphorylation-dependent conformational switch in the cellular autophagic process. (C) 2014 Elsevier B.V. All rights reserved.

A novel syndrome of severe neutrophil dysfunction: unresponsiveness confined to chemotaxin-induced functions.

We have identified a patient with a number of neutrophil dysfunctions. The patient was a female baby who lived for 8 months. During her life, she developed severe bacterial infections and showed omphalitis, impaired wound healing, and a pronounced leukocytosis. She was not a patient with leukocyte adhesion deficiency, because all leukocyte CD18 complex proteins were expressed at normal levels. Yet, neutrophil polarization and chemotaxis to platelet-activating factor, leukotriene B4, or formyl-methionyl-leucyl-phenylalanine (FMLP) were completely absent. We found a strong defect in actin polymerization in response to chemotactic stimuli, but only a retarded or even normal reaction with other stimuli. This indicates that the cellular dysfunctions were not due to an intrinsic defect in actin metabolism. Instead, the regulation of actin polymerization with chemotactic stimuli seemed to be defective. We concentrated on FMLP-induced responses in the patient's neutrophils. Functions dependent on activation of complement receptor type 3, such as aggregation or adherence to endothelial cells, were normally induced. Binding to serum-coated coverslips was normal in cell number; however, spreading was not observed. Exocytosis from the specific granules was readily induced. In contrast, FMLP failed to induce a respiratory burst activity or degranulation of the azurophil granules. FMLP induced a normal increase in free intracellular Ca2+, but a decreased formation of diglycerides (especially the 1-O-alkyl,2-acyl compounds). Thus, we have described a patient whose neutrophils show a severe defect in functional activation via chemotaxin receptors, resulting in a selective absence of NADPH oxidase activity, exocytosis from the azurophil granules, and actin polymerization. Our findings show that actin polymerization for neutrophil spreading and locomotion is regulated differently from that for phagocytosis. Also, the release of azurophil and specific granule contents is clearly shown to be regulated in a different way.