Studies of Phosphazenes. Part 13.' Thermal Rearrangement Reactions of Some Met hoxycyclo phosp hazenes

The methoxycyclophosphazenes [NP(OMe),], (n = 3-6) rearrange on heating to give oxocyclophosphazanes, [N(Me)PO(OMe)],. Isomeric products are formed when n = 4-6. The lH, ,lP, and 13C n.m.r. data for the starting materials and the products are presented. The ethoxy- and n-propoxy-derivatives N,P,( OR)* do not undergo the above rearrangement. The geminal derivatives N,P,R,(OMe), (R = Ph or NHBut) on heating yield both fully and partially rearranged products, namely dioxophosphaz-1 -enes and oxophosphazadienes, as shown by 270- MHz lH n.m.r. spectroscopy. The non-geminal derivative N,P,( NMe,),(OMe), gives only the fully rearranged product N,Me,P,(NMe,),O,(OMe), whose structure has been established from its lH and 31P n.m.r. spectra.

Photofragmentation Reactions Of Thiocarbonyl Compounds

Preferential yield of ring expansion and rearrangement products through α-cleavage of tetramethyl-3-thio-1,3-cyclobutanedione (1) and 3-mercapto-2,2,4-trimethyl-3-pentenoic acid β-(thio lactone) (2) involving diradical and carbene has been observed upon photolysis of 1 and 2.

Fast Iterative Division of p-adic Numbers

A fast iterative scheme based on the Newton method is described for finding the reciprocal of a finite segment p-adic numbers (Hensel code). The rate of generation of the reciprocal digits per step can be made quadratic or higher order by a proper choice of the starting value and the iterating function. The extension of this method to find the inverse transform of the Hensel code of a rational polynomial over a finite field is also indicated.

A global convergence criterion for discrete-time multivariable adaptive systems

The paper deals with the basic problem of adjusting a matrix gain in a discrete-time linear multivariable system. The object is to obtain a global convergence criterion, i.e. conditions under which a specified error signal asymptotically approaches zero and other signals in the system remain bounded for arbitrary initial conditions and for any bounded input to the system. It is shown that for a class of up-dating algorithms for the adjustable gain matrix, global convergence is crucially dependent on a transfer matrix G(z) which has a simple block diagram interpretation. When w(z)G(z) is strictly discrete positive real for a scalar w(z) such that w-1(z) is strictly proper with poles and zeros within the unit circle, an augmented error scheme is suggested and is proved to result in global convergence. The solution avoids feeding back a quadratic term as recommended in other schemes for single-input single-output systems.

Development of a stable isotope index to assess decadal-scale vegetation change and application to woodlands of the Burdekin catchment, Australia

Forty-four study sites were established in remnant woodland in the Burdekin River catchment in tropical north-east Queensland, Australia, to assess recent (decadal) vegetation change. The aim of this study was further to evaluate whether wide-scale vegetation 'thickening' (proliferation of woody plants in formerly more open woodlands) had occurred during the last century, coinciding with significant changes in land management. Soil samples from several depth intervals were size separated into different soil organic carbon (SOC) fractions, which differed from one another by chemical composition and turnover times. Tropical (C4) grasses dominate in the Burdekin catchment, and thus δ13C analyses of SOC fractions with different turnover times can be used to assess whether the relative proportion of trees (C3) and grasses (C4) had changed over time. However, a method was required to permit standardized assessment of the δ13C data for the individual sites within the 13 Mha catchment, which varied in soil and vegetation characteristics. Thus, an index was developed using data from three detailed study sites and global literature to standardize individual isotopic data from different soil depths and SOC fractions to reflect only the changed proportion of trees (C3) to grasses (C3) over decadal timescales. When applied to the 44 individual sites distributed throughout the Burdekin catchment, 64% of the sites were shown to have experienced decadal vegetation thickening, while 29% had remained stable and the remaining 7% had thinned. Thus, the development of this index enabled regional scale assessment and comparison of decadal vegetation patterns without having to rely on prior knowledge of vegetation changes or aerial photography.

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

Psychological consequences of cancer from the salutogenic and dyadic perspective

Previous empirical research has shown that positive, i.e. salutogenic, psychological resources and social support, have health-promoting effects in stressful life situations. In the present study the associations between sense of coherence (SOC), dispositional optimism, partner support, psychological distress, and quality of life among cancer patients and their partners were examined. The data was collected from Helsinki University Central Hospital in 1997 2000 by self-report questionnaires approximately 2, 8, and 14 months post diagnosis. Participants in studies I-IV were 155, 123, 153, and 147 cancer patients and their partners, respectively. The sample of the present study consisted of physically relatively well-functioning patients, whose overall psychological wellbeing was generally good as compared to the healthy population. Partners in this study, however, reacted more strongly to their partners illness and treatment. The partners displayed e.g. higher levels of anxiety and depression than the patients. The results of this study indicated that cancer patients and their partners with strong SOC and who are optimistic report fewer symptoms of distress. Moreover, patients who display an optimistic attitude to life, who receive support from their partner, and who control how they express anger have a better quality of life. The findings also confirmed that the role of the partner is significant in coping with cancer. The symptoms of depression and anxiety in patients and partners were associated, and the partner s optimism seemed to protect also the patient from elevated levels of anxiety. The role of the partner was also highlighted in the couples anger-expression styles. The patients and partners tendency to inhibit anger was associated with decreased partner support and worse patient quality of life. Finally, in the present study we found substantial gender differences. For the patients, partner support was more significant for the women than for the men. Furthermore, for the female patients, the husband s tendency to openly express anger (anger-out) had a negative impact on their psychological quality of life, whereas the wives high anger-out seemed to predict good psychological quality of life in the men. Also, in this study the female partners reported higher levels of anxiety and depression as compared to the male partners. The results of the present study extend the previous literature on positive psychological resources and psychological wellbeing among cancer couples. Furthermore, these findings support the theory on SOC and optimism as health-promoting factors. However, the construct of SOC seems to include other important elements besides optimism. The findings of this study are applicable in designing new rehabilitation programmes for cancer patients and their partners.

Mesoscale description of an asymmetric lamellar phase

The relationship between the parameters in a description based on a mesoscale free energy functional for the concentration field and the macroscopic properties, such as the bending and compression moduli and the permeation constant, are examined for an asymmetric lamellar phase where the mass fractions of the hydrophobic and hydrophilic parts are not equal. The difference in the mass fractions is incorporated using a cubic term in the free energy functional, in addition to the usual quadratic and quartic terms in the Landau–Ginsburg formulation. The relationship between the coefficient of the cubic term and the difference in the mass fractions of the hydrophilic and hydrophobic parts is obtained. For a lamellar phase, it is important to ensure that the surface tension is zero due to symmetry considerations. The relationship between the parameters in the free energy functional for zero surface tension is derived. When the interface between the hydrophilic and hydrophobic parts is diffuse, it is found that the bending and compression moduli, scaled by the parameters in the free energy functional, do increase as the asymmetry in the bilayer increases. When the interface between the hydrophilic and hydrophobic parts is sharp, the scaled bending and compression moduli show no dependence on the asymmetry in the bilayer. The ratio of the permeation constant in between the water and bilayer in a molecular description and the Onsager coefficient in the mesoscale description is O(1) for both sharp and diffuse interfaces and it increases as the difference in the mass fractions is increased.

Developmental origins of psychological vulnerability factors for mental disorders

Premature birth and associated small body size are known to affect health over the life course. Moreover, compelling evidence suggests that birth size throughout its whole range of variation is inversely associated with risk for cardiovascular disease and type 2 diabetes in subsequent life. To explain these findings, the Developmental Origins of Health and Disease (DOHaD) model has been introduced. Within this framework, restricted physical growth is, to a large extent, considered either a product of harmful environmental influences, such as suboptimal nutrition and alterations in the foetal hormonal milieu, or an adaptive reaction to the environment. Whether inverse associations exist between body size at birth and psychological vulnerability factors for mental disorders is poorly known. Thus, the aim of this thesis was to study in three large prospective cohorts whether prenatal and postnatal physical growth, across the whole range of variation, is associated with subsequent temperament/personality traits and psychological symptoms that are considered vulnerability factors for mental disorders. Weight and length at birth in full term infants showed quadratic associations with the temperamental trait of harm avoidance (Study I). The highest scores were characteristic of the smallest individuals, followed by the heaviest/longest. Linear associations between birth size and psychological outcomes were found such that lower weight and thinness at birth predicted more pronounced trait anxiety in late adulthood (Study II); lower birth weight, placental size, and head circumference at 12 months predicted a more pronounced positive schitzotypal trait in women (Study III); and thinness and smaller head circumference at birth associated with symptoms of attention-deficit hyperactivity disorder (ADHD) in children who were born at term (Study IV). These associations occured across the whole variation in birth size and after adjusting for several confounders. With respect to growth after birth, individuals with high trait anxiety scores in late adulthood were lighter in weight and thinner in infancy, and gained weight more rapidly between 7 and 11 years of age, but weighed less and were shorter in late adulthood in relation to weight and height measured at 11 years of age (Study II). These results suggest that a suboptimal prenatal environment reflected in smaller birth size may affect a variety of psychological vulnerability factors for mental disorders, such as the temperamental trait of harm avoidance, trait anxiety, schizotypal traits, and symptoms of ADHD. The smaller the birth size across the whole range of variation, the more pronounced were these psychological vulnerability factors. Moreover, some of these outcomes, such as trait anxiety, were also predicted by patterns of growth after birth. The findings are concordant with the DOHaD model, and emphasise the importance of prenatal factors in the aetiology of not only mental disorders but also their psychological vulnerability factors.

Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Proline ring conformations corresponding to a bistable jump model from 13C spin-lattice relaxation times

A formalism for extracting the conformations of a proline ring based on the bistable jump model of R. E. London [(1978) J. Am. Chem. Soc. 100, 2678-2685] from 13C spin-lattice relaxation times (T1) is given. The method is such that the relaxation data are only partially used to generate the conformations; these conformations are constrained to satisfy the rest of the relaxation data and to yield acceptable ring geometry. An alternate equation for T1 of 13C nuclei to that of London is given. The formalism is illustrated through an example.

Double-authentication-preventing signatures

Digital signatures are often used by trusted authorities to make unique bindings between a subject and a digital object; for example, certificate authorities certify a public key belongs to a domain name, and time-stamping authorities certify that a certain piece of information existed at a certain time. Traditional digital signature schemes however impose no uniqueness conditions, so a trusted authority could make multiple certifications for the same subject but different objects, be it intentionally, by accident, or following a (legal or illegal) coercion. We propose the notion of a double-authentication-preventing signature, in which a value to be signed is split into two parts: a subject and a message. If a signer ever signs two different messages for the same subject, enough information is revealed to allow anyone to compute valid signatures on behalf of the signer. This double-signature forgeability property discourages signers from misbehaving—a form of self-enforcement—and would give binding authorities like CAs some cryptographic arguments to resist legal coercion. We give a generic construction using a new type of trapdoor functions with extractability properties, which we show can be instantiated using the group of sign-agnostic quadratic residues modulo a Blum integer; we show an additional application of these new extractable trapdoor functions to standard digital signatures.

Hardness Methods for Testing Maize Kernels

Maize is a highly important crop to many countries around the world, through the sale of the maize crop to domestic processors and subsequent production of maize products and also provides a staple food to subsistance farms in undeveloped countries. In many countries, there have been long-term research efforts to develop a suitable hardness method that could assist the maize industry in improving efficiency in processing as well as possibly providing a quality specification for maize growers, which could attract a premium. This paper focuses specifically on hardness and reviews a number of methodologies as well as important biochemical aspects of maize that contribute to maize hardness used internationally. Numerous foods are produced from maize, and hardness has been described as having an impact on food quality. However, the basis of hardness and measurement of hardness are very general and would apply to any use of maize from any country. From the published literature, it would appear that one of the simpler methods used to measure hardness is a grinding step followed by a sieving step, using multiple sieve sizes. This would allow the range in hardness within a sample as well as average particle size and/or coarse/fine ratio to be calculated. Any of these parameters could easily be used as reference values for the development of near-infrared (NIR) spectroscopy calibrations. The development of precise NIR calibrations will provide an excellent tool for breeders, handlers, and processors to deliver specific cultivars in the case of growers and bulk loads in the case of handlers, thereby ensuring the most efficient use of maize by domestic and international processors. This paper also considers previous research describing the biochemical aspects of maize that have been related to maize hardness. Both starch and protein affect hardness, with most research focusing on the storage proteins (zeins). Both the content and composition of the zein fractions affect hardness. Genotypes and growing environment influence the final protein and starch content and. to a lesser extent, composition. However, hardness is a highly heritable trait and, hence, when a desirable level of hardness is finally agreed upon, the breeders will quickly be able to produce material with the hardness levels required by the industry.

Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.

Single layer bismuth iodide: Computational exploration of structural, electrical, mechanical and optical properties

Layered graphitic materials exhibit new intriguing electronic structure and the search for new types of two-dimensional (2D) monolayer is of importance for the fabrication of next generation miniature electronic and optoelectronic devices. By means of density functional theory (DFT) computations, we investigated in detail the structural, electronic, mechanical and optical properties of the single-layer bismuth iodide (BiI3) nanosheet. Monolayer BiI3 is dynamically stable as confirmed by the computed phonon spectrum. The cleavage energy (Ecl) and interlayer coupling strength of bulk BiI3 are comparable to the experimental values of graphite, which indicates that the exfoliation of BiI3 is highly feasible. The obtained stress-strain curve shows that the BiI3 nanosheet is a brittle material with a breaking strain of 13%. The BiI3 monolayer has an indirect band gap of 1.57 eV with spin orbit coupling (SOC), indicating its potential application for solar cells. Furthermore, the band gap of BiI3 monolayer can be modulated by biaxial strain. Most interestingly, interfacing electrically active graphene with monolayer BiI3 nanosheet leads to enhanced light absorption compared to that in pure monolayer BiI3 nanosheet, highlighting its great potential applications in photonics and photovoltaic solar cells.