The Absolute Subspace Theorem and linear equations with unknowns from a multiplicative group

The absolute tensorial energy density equation of a momentless elastic solid is studied. The energy density concept is developed in arbitrary non-cartesian curvilinear coordinates and the final equation is applicable to theories such as those developed for beams, plates or shells. The use of the Trefftz’s method in connection with the absolute energy density equation will allow us to obtain the following: the non-linear equations of equilibrium, the stability condition, the post-buckling equation and a fourth order functional related to the fourth variation of the energy density equation for an elastic solid.

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Linear Equations in Variables which Lie in a Multiplicative Group

Annals of Mathematics ◽

10.2307/3062133 ◽

2002 ◽

Vol 155 (3) ◽

pp. 807 ◽

Cited By ~ 73

Author(s):

J.-H. Evertse ◽

H. P. Schlickewei ◽

W. M. Schmidt

Keyword(s):

Multiplicative Group ◽

Linear Equations

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Linear equations with unknowns from a multiplicative group in a function field

Acta Arithmetica ◽

10.4064/aa133-2-4 ◽

2008 ◽

Vol 133 (2) ◽

pp. 159-170 ◽

Cited By ~ 2

Author(s):

Jan-Hendrik Evertse ◽

Umberto Zannier

Keyword(s):

Function Field ◽

Multiplicative Group ◽

Linear Equations

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Bulk standards for low-temperature biological x-ray microanalysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100111525 ◽

1984 ◽

Vol 42 ◽

pp. 282-283

Author(s):

P. Echlin ◽

M. McKoon ◽

E.S. Taylor ◽

C.E. Thomas ◽

K.L. Maloney ◽

...

Keyword(s):

Phase Separation ◽

Low Temperature ◽

Analytical Method ◽

Salt Solutions ◽

Absolute Concentration ◽

Cooling Process ◽

X Ray ◽

The Absolute ◽

Analytical Procedures ◽

Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

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A Quantitative Ultrastructural Study of Peripheral Blood Lymphocytes Containing Parallel Tubular Arrays in Epstein-Barr Virus and Cytomegalo-Virus Mononucleosis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100098769 ◽

1981 ◽

Vol 39 ◽

pp. 454-455

Author(s):

C. M. Payne ◽

P. M. Tennican

Keyword(s):

Peripheral Blood ◽

Lymphocyte Count ◽

Epstein Barr Virus ◽

Absolute Lymphocyte Count ◽

Peripheral Blood Lymphocytes ◽

Clinical State ◽

Barr Virus ◽

The Absolute ◽

Epstein Barr ◽

Tubular Arrays

In the normal peripheral circulation there exists a sub-population of lymphocytes which is ultrastructurally distinct. This lymphocyte is identified under the electron microscope by the presence of cytoplasmic microtubular-like inclusions called parallel tubular arrays (PTA) (Figure 1), and contains Fc-receptors for cytophilic antibody. In this study, lymphocytes containing PTA (PTA-lymphocytes) were quantitated from serial peripheral blood specimens obtained from two patients with Epstein -Barr Virus mononucleosis and two patients with cytomegalovirus mononucleosis. This data was then correlated with the clinical state of the patient.It was determined that both the percentage and absolute number of PTA- lymphocytes was highest during the acute phase of the illness. In follow-up specimens, three of the four patients' absolute lymphocyte count fell to within normal limits before the absolute PTA-lymphocyte count.In one patient who was followed for almost a year, the absolute PTA- lymphocyte count was consistently elevated (Figure 2). The estimation of absolute PTA-lymphocyte counts was determined to be valid after a morphometric analysis of the cellular areas occupied by PTA during the acute and convalescent phases of the disease revealed no statistical differences.

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Polarity Determination in Sphalerite and Wurtzite Structures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100136106 ◽

1990 ◽

Vol 48 (2) ◽

pp. 500-501

Author(s):

Stuart McKernan ◽

C. Barry Carter

Keyword(s):

Opposite Polarity ◽

Single Domain ◽

Polar Material ◽

Electron Microscopic ◽

Dynamical Interaction ◽

X Ray ◽

Polarity Determination ◽

The Absolute ◽

Microscopic Techniques

The determination of the absolute polarity of a polar material is often crucial to the understanding of the defects which occur in such materials. Several methods exist by which this determination may be performed. In bulk, single-domain specimens, macroscopic techniques may be used, such as the different etching behavior, using the appropriate etchant, of surfaces with opposite polarity. X-ray measurements under conditions where Friedel’s law (which means that the intensity of reflections from planes of opposite polarity are indistinguishable) breaks down can also be used to determine the absolute polarity of bulk, single-domain specimens. On the microscopic scale, and particularly where antiphase boundaries (APBs), which separate regions of opposite polarity exist, electron microscopic techniques must be employed. Two techniques are commonly practised; the first [1], involves the dynamical interaction of hoLz lines which interfere constructively or destructively with the zero order reflection, depending on the crystal polarity. The crystal polarity can therefore be directly deduced from the relative intensity of these interactions.

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