Some characterisations of supported algebras

We give several equivalent characterisations of left (and hence, by duality, also of right) supported algebras. These characterisations are in terms of properties of the left and the right parts of the module category, or in terms of the classes L₀ and R₀ which consist respectively of the predecessors of the projective modules, and of the successors of the injective modules.     

Regarding the structure of [2.2](2,6,2',7')-naphthalenophane-1,11-diene and its conformational mobility

The synthesis of [2.2](2,6,2',7')naphthalenophane -1,11 - diene 4 has been effected by pyrolysis of the bis-sulphoxide 10, in turn prepared by a ring-contraction procedure of the [3.3]dithiacyclophane 7. The diene 4 has been fully characterized by spectroscopic and chemical methods. The variable-temperature ¹H NMR spectra of the diene 4 indicated that the compound undergoes conformational flipping in solution and has a conformational energy barrier ΔG^≠_25°. 14.9 kcal mol^-1 and a coalescence temperature T_c 38° for the internal protons H_c and H_c' (at 100 MHz). These results differ from those previously recorded. A complete assignment of the pmr spectrum of the cyclophane diene 4 at 270 MHz is presented together with the spectrum of the corresponding saturated [2.2]cyclophane 3.     

Materials and Methods

Materials and Methods Synthesis of thionyl chloride-activated succinamidopropyl-glass beads     

A convenient synthesis of 3-aryl-1,2,4-triazolo[4,3-c]quinazolines

The synthesis and characterization of several 3-aryl-1,2,4-triazolo[4,3-c]quinazolines is described. The first step comprises the condensation of aromatic aldehydes with 2-(H or Cl)-4-hydrazinoquinazolines 2 to afford the corresponding hydrazones 3 . The second step involves the cyclization to the title compounds 4 in bromine/acetic acid. Reaction of 4 (X = Cl) with cyclic amines gave the corresponding 5-cyclicamino 5 or 5-alkoxy derivatives 6 .     

Polymeric p-benzoquinone–tin derivatives as thermal stabilizers for rigid poly(vinyl chloride). II. Evaluation of the stabilizing efficiency

The polymeric p-benzoquinone-tin derivatives obtained from the reaction of p-benzoquinone with tin tetrachloride in the absence of solvent have been investigated as thermal stabilizers for rigid PVC at 200°C by measuring the rate of dehydrochlorination. The results reveal the greater stabilizing efficiency of the investigated products in relation to dibutyltin maleate and the basic lead stabilizers commonly used in industry. Evidence has been accumulated that the quinone and metallic elements (Sn? Sn bonds) of the stabilizer participate in the stabilization process by trapping the radical intermediates of degradation and blocking the odd electron sites formed on the polymer chains. Although stabilizers with high quinone content provide greater stabilization in the early stages of degradation, their efficiency sharply decreases in subsequent stages. On the other hand, stabilizers of high tin content effectively prohibit the dehydrochlorination reaction at all stages of degradation. On an equivalent basis of metal content, the results clearly demonstrate the greater stabilizing efficiency of tin atoms when found in direct contact in the stabilizer molecule. The mechanism of stabilization suggested to account for the results obtained may be considered as additional evidence in support of the radical nature of the dehydrochlorination reaction.     

The raised-cosine wavelets in computerized tomography

In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. The rate of convergence of the resulting algorithm to the image density function is found under suitable hypotheses. This algorithm is then tested on the standard Shepp–Logan     

Polynomials: a theme which should not be forgotten

There is a definite movement to remove many of the topics concerning polynomials from the school curriculum. The purpose of this paper is to point out why this movement is misguided and should be reversed.     

Sloshing waves in a heated viscoelastic fluid layer in an excited rectangular tank

In this paper, we have investigated the motion of a heated viscoelastic fluid layer in a rectangular tank that is subjected to a horizontal periodic oscillation. The mathematical model of the current problem is communicated with the linearized Navier–Stokes equation of the viscoelastic fluid and heat equation together with the boundary conditions that are solved by means of Laplace transform. Time domain solutions are consequently computed by using Durbin's numerical inverse Laplace transform scheme. Various numerical results are provided and thereby illustrated graphically to show the effects of the physical parameters on the free-surface elevation time histories and heat distribution. The numerical applications revealed that increasing the Reynolds number as well as the relaxation time parameter leads to a wider range of variation of the free-surface elevation, especially for the short time history.     

Mathematical attitudes and semantic differentials

The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics.