The Legendre Formula in Clifford Analysis

2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.

Clifford-Hermite polynomials in fractional Clifford analysis

In this paper we generalize radial and standard Clifford-Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann-Liouville derivative in a symbolic way. As main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven.

Recurrence relations for Clifford algebra-valued orthogonal polynomials

The theory of orthogonal polynomials of one real or complex variable is well established as well as its generalization for the multidimensional case. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with higher dimensions. In this context, we study systems of orthogonal polynomials of a hypercomplex variable with values in a Clifford algebra and prove some of their properties.

LC-MSn analysis of the cis isomers of chlorogenic acids

The behaviour of cis isomers of selected mono- and di-acyl chlorogenic acids produced by UV-irradiation has been investigated by LC-MSn. cis Isomers fragment identically to the more common trans isomers. cis-5-Acyl chlorogenic acids are more hydrophobic and elute later than their mono- or di-trans counterparts whereas the reverse is true for cis-3-acyl and cis-4-acyl chlorogenic acids. The cis isomers of 1,3-dicaffeoylquinic acid, the only I-acyl chlorogenic acid investigated, are also more hydrophobic than the di-trans isomer. Coffee leaves had a proportionately greater content of cis isomers relative to trans isomers compared with coffee beans suggesting that UV-irradiation in vivo may also cause geometric isomerisation. (c) 2007 Elsevier Ltd. All rights reserved.

Fermionic analysis of Davey-Stewartson dromions

Dromion solutions of the Davey-Stewartson equation are analysed from the point of view of the bilinear formalism. The corresponding τ-functions are expressed in terms of vacuum expectation values of Clifford operators and their group-theoretical content is provided. Explicit computation performed with the help of Wick's theorem allows us to characterize the dromion interaction. © 1990.

Spectrographic Analysis of Montana Limestones

Spectrographic analysis of limestones as a possible method of correlation of geologic formations is an altogether new line of investigation. As far as known the only previous work consists of a few analyses made by Fred Lines in his bachelor thesis work at Montana School of mines in the spring of 1942.

Analysis of endogenous retinoic acid receptor expression and function in murine melanoma cells

There have been numerous reports over the past several years on the ability of vitamin A analogs (retinoids) to modulate cell proliferation, malignant transformation, morphogenesis, and differentiation in a wide variety of cell types and organisms. Two families of nuclear retinoid-inducible, trans-acting, transcription-enhancing receptors that bear strong DNA sequence homology to thyroid and steroid hormone receptors have recently been discovered. The retinoic acid receptors (RARs) and retinoid X receptors (RXRs) each have at least three types designated $\alpha,$ $\beta,$ and $\gamma,$ which are encoded by separate genes and expressed in a tissue and cell type-specific manner. We have been interested in the mechanism by which retinoids inhibit tumor cell proliferation and induce differentiation. As a model system we have employed several murine melanoma cell lines (S91-C2, K1735P, and B16-F1), which are sensitive to the growth-inhibitory and differentiation-inducing effects of RA, as well as a RA-resistant subclone of one of the cell lines (S91-C154), in order to study the role of the nuclear RARs in these effects. The initial phase of this project consisted of the characterization of the expression pattern of the three known RAR and RXR types in the murine melanoma cell lines in order to determine whether any differences exist which may elucidate a role for any of the receptors in RA-induced growth inhibition and differentiation. The novel finding was made that the RAR-$\beta$ gene is rapidly induced from undetectable levels by RA treatment at the mRNA and protein level, and that the induction of RAR-$\beta$ by other biologically active retinoids correlated with their ability to inhibit the growth of the highly RA-sensitive S91-C2 cell line. This suggests a role for RAR-$\beta$ in the growth inhibiting effect of retinoids. The second phase of this project involves the stable expression of RAR-$\beta$ in the S91-C2 cells and the RAR-$\beta$ receptor-null cell line, K1735P. These studies have indicated an inverse correlation between RAR-$\beta$ expression and proliferation rate. ^

Organization and staffing for full-time local health services; analysis of information submitted to the Public Health Service in Report of public health personnel as of December 31, 1954.

Mode of access: Internet.

Analysis of mixed paints,

Mode of access: Internet.

Organization and staffing for local health services; analysis of information submitted to the Public Health Service in Report of public Health personnel as of January 1, 1958.

Mode of access: Internet.

Analysis of statically indeterminate structures.

Mode of access: Internet.

Hispanic -serving land -grant colleges: Analysis and plan for an educational policy initiative

Hispanics and other minority Americans are denied access to higher education by a system that needs structural reform. The purpose of the research was to determine whether creating Hispanic-serving land-grant colleges, similar to the Morrill land-grant colleges serving Black and Native Americans, might be an effective strategy to increase the access of Hispanic students to quality higher education. In addition to published materials, data was collected from a survey of Hispanic-serving institutions and extensive interviews with college presidents, government representatives, educational association leaders, and educational historians. ^ The research examined how existing land-grant college systems came into being and how they have evolved. A look at the functions of the land-grant systems serving Blacks and Native Americans revealed promising possibilities for a system that would include more Hispanics. Legal, fiscal, curricular, and organizational criteria were inferred from the existing systems. While none of the existing land-grant systems can be adapted to serve Hispanics or most other minorities outside their limited regions, each has elements that could be adapted by a new minority-serving system. A number of colleges already have features that could make them candidates for state designation as land-grant colleges. ^ The research suggests that a new federally funded system of Morrill land-grant colleges dedicated to serving all urban Americans, not just Hispanics, would do much to increase the numbers of Hispanic students and other racially and ethnically minority Americans in good quality higher educational institutions. An inclusive urban land-grant system would be politically feasible, whereas one meant to serve Hispanics alone would not. Because of their urban locations, these universities would serve large concentrations of minority citizens of all ethnic groups. ^ Finally, the basic elements of a strategic plan are presented for an educational organization to use for organizing leaders of minority educational associations, financing an initiative to lobby Congress, eliciting legislative and federal agency support, and securing the assistance of other educational, industrial, and special interest groups. The plan includes a suggested timetable for action. Recommendations are made for innovations that would make such a higher education system distinctive and would help meet important national needs. ^

Analysis Of The Dna Fourier Transform-infrared Microspectroscopic Signature Using An All-reflecting Objective.

The Fourier transform-infrared (FT-IR) signature of dry samples of DNA and DNA-polypeptide complexes, as studied by IR microspectroscopy using a diamond attenuated total reflection (ATR) objective, has revealed important discriminatory characteristics relative to the PO2(-) vibrational stretchings. However, DNA IR marks that provide information on the sample's richness in hydrogen bonds have not been resolved in the spectral profiles obtained with this objective. Here we investigated the performance of an all reflecting objective (ARO) for analysis of the FT-IR signal of hydrogen bonds in DNA samples differing in base richness types (salmon testis vs calf thymus). The results obtained using the ARO indicate prominent band peaks at the spectral region representative of the vibration of nitrogenous base hydrogen bonds and of NH and NH2 groups. The band areas at this spectral region differ in agreement with the DNA base richness type when using the ARO. A peak assigned to adenine was more evident in the AT-rich salmon DNA using either the ARO or the ATR objective. It is concluded that, for the discrimination of DNA IR hydrogen bond vibrations associated with varying base type proportions, the use of an ARO is recommended.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.