Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

The surface electromyography-force relationship during isometric dorsiflexion in males and females

This study evaluated sex-related differences in the tibialis anterior (TA) surface electromyography (EMG) to force relationship. One-hundred participants (50 males and 50 females) performed three isometric contractions at 20, 40, 60, 80, and 100% of maximal voluntary contraction (MVC) in an apparatus designed to isolate the action of the dorsiflexors. The surface EMG signal was amplified (lOOOx), band-pass filtered (10-500Hz), and sampled at 2048 Hz. The load cell signal was low-passed filtered at 100 Hz and sampled at the same rate. Males were stronger than females {P <0.05). However, there was no significant difference in root-mean-square (RMS) values between sexes {P <0.05). Both sexes exhibited a quadratic increase in RMS across force levels (P <0.05). The mean power frequency (MNF) for males was greater than for females {P <0.05). Males and females exhibited a linear increase in both frequency measures up to 80% of MVC (P <0.05). Between 80 and 100% MVC, the frequency values for the females plateaued while males showed a decrease {P <0.05). The magnitude of the difference in MNF between males and females was consistent with sex-specific TA physiology. In general, the pattern of means for RMS and MNF between males and females revealed no sex-related differences in the surface EMG/force relationship. We therefore conclude that there are no sex-related differences in the gradation of muscle force.

Cognitive set, absorption, and achievement as moderators of the perceptual closure effect in picture priming /

The present study examined individual differences in Absorption and fantasy, as well as in Achiievement and achievement striving as possible moderators of the perceptual closure effect found by Snodgrass and Feenan (1990). The study also examined whether different instructions (experiential versus instrumental) interact with the personality variables to moderate the relationship between priming and subsequent performance on a picture completion task. 1 28 participants completed two sessions, one to fill out the MPQ and NEO personality inventories and the other to complete the experimental task. The experimental task consisted of a priming phase and a test phase, with pictures presented on a computer screen for both phases. Participants were shown 30 pictures in the priming phase, and then shovm the 30 primed pictures along with 30 new pictures for the test phase. Participants were randomly assigned to receive one of the two different instruction sets for the task. Two measures of performance were calculated, most fragmented measure and threshold. Results of the present study confirm that a five-second exposure time is long enough to produce the perceptual closure effect. The analysis of the two-way interaction effects indicated a significant quadratic interaction of Absorption with priming level on threshold performance. The results were in the opposite direction of predictions. Possible explanations for the Absorption results include lack of optimal conditions, lack of intrinsic motivation and measurement problems. Primary analyses also revealed two significant between-subject effects of fantasy and achievement striving on performance collapsed across priming levels. These results suggest that fantasy has a beneficial effect on performance at test for pictures primed at all levels, whereas achievement striving seems to have an adverse effect on performance at test for pictures primed at all levels. Results of the secondary analyses with a revised threshold performance measure indicated a significant quadratic interaction of Absorption, condition and priming level. In the experiential condition, test performance, based on Absorption scores for pictures primed at level 4, showed a positive slope and performance for pictures primed at levels 1 and 7 based on Absorption showed a negative slope. The reverse effect was found in the instrumental condition. The results suggest that Absorption, in combination with experiential involvement, may affect implicit memory. A second significant result of the secondary analyses was a linear three-way interaction of Achievement, condition and priming level on performance. Results suggest that as Achievement scores increased, test performance improved for less fragmented primed pictures in the instrumental condition and test performance improved for more highly fragmented primes in the experiential condition. Results from the secondary analyses suggest that the revised threshold measure may be more sensitive to individual differences. Results of the exploratory analyses with Openness to Experience, Conscientiousness and agentic positive emotionality (PEM-A) measures indicated no significant effects of any of these personality variables. Results suggest that facets of the scales may be more useful with regard to perceptual research, and that future research should examine narrowly focused personality traits as opposed to broader constructs.

Analysis Of The A11a22 X 11a11 And A 33a22 X 1 electronic transitions in selenocarbonyl difluoride

The absorption spectrum of F2CSe in the 18800-21900 cm-1 region has been recorded at -770 C and 220 C under the conditions of medium resolution. The responsible electronic promotion is TI* + n excitation which leads to 3A2 and lA2 excited states. Progressions in vI', v2', v3" v4' and v4" have been identified in the spectrum and have been analyzed in terms of vibronic transitions between a planar ground state and a nQnplanar excited state. The - 3 - 1 - 1 - 1 origins of the a A2 + X Al and A A2 + X Al systems were assigned to the bands at 19018 cm-l and 19689 cm-l . This has given a singlet-triplet splittl. n g lA2 - 3A2 P f 671 cm -1 The out-of-plane wagging levels were found to be anharmonic. 1 -1 Barrier heights of 2483 cm- and 2923 cm were obtained for the lA2 and 3A2 upper states from a fitting of the energy levels of a Lorentzian-quadratic function to the observed levels in the out-of-plane wagging modes. 1 3 For the A2 and A2 states nonplanar equilibrium angles of 30.10 and 31.40 have been evaluated respectively. i

Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.