Geometric Induction Research Articles

Errors in average strength estimates of sedimentary rock masses in South Yakutia based on geometric induction sounding data

The probabilistic model developed to describe the engineering and geological conditions for the operation of buildings and infrastructure in the city of Neryungri has been verified. The model is a power-function equation which correlates, by regression relationships, laboratory-determined compressive strength of saturated frozen sandstone samples with attenuation of the high-frequency harmonic field of a vertical magnetic dipole in warm permafrost composed of sandstone. The attenuation values were obtained by geometric electromagnetic induction sounding at a frequency of 1.125 MHz. The model verification was conducted at a fixed frequency on a section of the Amur-Yakutsk Railway located at a significant distance from Neryungri. The railway here is underlain by low-temperature dolomite masses. The statistical analysis indicates that the relative errors of the dolomite saturated strength estimates from the geometric EM induction data with a 73.0% probability do not exceed 20%. With this level of accuracy close to that of laboratory tests according to GOST 25100–2020, it is reasonable to suggest that the probabilistic model can be used region-wide in southern Yakutia to predict saturated strength of foundation materials composed of sandstone and dolomite. It can provide an effective solution for market-based construction and mining industries, as increasing anthropogenic and climatic impacts are anticipated to cause thawing and saturation of sedimentary rock masses.

Mapping capabilities of geometric EM induction sounding in southern Yakutia permafrost

The purpose of the article is to consider the possibilities of the geophysical method in solving the problem of quantitative estimation of the strength of sedimentary rocks that form the basis of engineering structures at the Kyurgellakh station of the Amur-Yakutsk Railway located 572 km away from the town of Neryungri, which is an administrative center of southern Yakutia (Russia). The problem is solved using the method of geometric electromagnetic induction sounding and a new technique that explored the attenuation of the harmonic field induced by a vertical magnetic dipole in the inhomogeneous anisotropic geological medium at the frequencies of 1.125 and 0.281 MHz in the intermediate separation zone of 5–100 m. A comparative analysis has determined a good agreement in changes of geological and geophysical estimates of the average strength of laboratory water-saturated samples and sedimentary rock mass predicted in the same state at the comparable depth of 6–12 m. The measure of agreement when using the most adequate equation of the power function is high and equals 0.815 according to the normalized coefficient of multiple determination. This means that strength is the most important factor among the frozen ground characteristics affecting the electromagnetic field attenuation at the frequencies and spacing specified, contributing no less than 80 %. The tested geophysical method can thus correctly map the distribution boundaries of different strength sedimentary rocks. The crushed and fissured rocks with the strengths below 40–35 MPa are confined to the tectonic fractures of varying directions with a polygon-like structure. Geophysical data clearly delineate the structure at the depths of 12.3–27.5 m where predominate the rocks with high strengths (50–120 MPa). The geometric EM induction sounding is recommended to use at all stages of geotechnical investigations to map the development areas of southern Yakutia by rock strength classes.

Geometric Induction in Chiral Superfluids.

We explore the properties of chiral superfluid thin films coating a curved surface. Because of the vector nature of the order parameter, a geometric gauge field emerges and leads to a number of observable effects such as anomalous vortex-geometric interaction and curvature-induced mass and spin supercurrents. We apply our theory to several well-known phases of chiral superfluid ^{3}He and derive experimentally observable signatures. We further discuss the cases of flexible geometries where a soft surface can adapt itself to compensate for the strain from the chiral superfluid. The proposed interplay between geometry and chiral superfluid order provides a fascinating avenue to control and manipulate quantum states with strain.

Maxwell field in spatially flat FLRW space-times

The classical and quantum theory of the Maxwell free field (or perturbation) minimally coupled to the gravity of local-Minkowskian spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) space-times is constructed in conformal local charts (herein called frames) where the Maxwell equations have the same form as in special relativity. Taking into account that the conformal coordinates cannot be measured directly, all the obtained results are transformed in physical frames, with cosmic time and space coordinates of Painlevé type, where these may take on a physical meaning. In these frames, the Maxwell theory is equivalent to the electrodynamics in flat macroscopic media whose constitutive equations predict magnetoelectric type effects interpreted here as a geometric induction. The given example is of a system of static charges giving rise simultaneously to time-dependent electric and magnetic fields that can be measured in physical frames. The quantization of the Maxwell free field in these manifolds is performed in a canonical manner using the momentum-helicity basis. The propagators in conformal and physical frames and the principal one-particle operators are written down. It is shown that this approach reveals a new behaviour of the one-particle wave packets during propagation and specific effects produced by the apparent horizons of the observers staying at rest in their proper physical frames.

Geometric Induction in Chiral Superconductors.

We consider a number of effects due to the interplay of superconductivity, electromagnetism, and elasticity, which are unique for thin membranes of layered chiral superconductors. Some of them should be within the reach of present technology, and could be useful for characterizing materials. More speculatively, the enriched control of Josephson junctions they afford might find useful applications.

Introduction to Discrete Mathematics and Fourier Analysis. A Practical Guide for third Year Undergraduate Students.

This book covers a quick introduction to high school mathematics, arithmetic and geometric series, infinite geometric series, mathematical induction, binomial theorem, factorials, permutations and combinations, determinants, systems of linear equations, boolean algebra, orthogonal functions, Legendre, Hermite, and Laguerre polynomials and orthogonal properties. For example, mathematical induction is a proof based on logical assumptions of equations that involve integers of one number that shows the proof for the next number. It is based on the base step and the inductive step. The base step is to prove the integers based on a formula. The inductive step involves statement of one integer number that shows the proof of the statement for the next integer. The determinant is a scalar and it is found by multiplying the two elements of the principal diagonal and subtracting them from the multiplication of the elements of the other diagonal.

Ab Initio Calculations of the Interaction between CO2 and the Acetate Ion

A series of ab initio calculations designed to investigate the interaction of CO(2) with acetate are presented. The lowest energy structure, AC-CO(2)-η(2), is predicted by CCSD(T)/aVTZ to be bound by -10.6 kcal/mol. Six of the bound complexes have binding energies on the order of -8 kcal/mol, but analysis shows that the η(1)-CT complex is fundamentally different from the others. The η(1)-CT complex is characterized by geometric distortion, large polarization and induction effects and charge transfer whereas the other five complexes have little geometric distortion and negligible charge transfer. The amount of charge that is transferred from the anion to the CO(2) in the η(1)-CT complex is estimated to be about half an electron by NPA, DMA, CHELPG, and Mulliken analyses, whereas the EDA-ALMO-CTA (B3LYP) approach predicts a charge transfer of 75 me(-). However, the transfer of this small amount of charge leads to an energy lowering of -56 kcal/mol, without which the complex would not be bound. The RI-MP2 geometries closely approximate those resulting from the CCSD optimizations, and the optimized second-order opposite spin (O2) method performs well for all the complexes except for the η(1)-CT complex. DFT methods do not reproduce all the ab initio geometries, binding energies and/or energy ordering of these complexes although the range-separated hybrid meta-GGA (M11) and nonlocal (VV10 and vdwDF10) functionals are shown to yield results significantly better than other functionals considered for this system. The fact that there is such variation among DFT methods has implications for DFT-based ab initio molecular dynamics simulations and for the parametrization of classical force fields based on DFT calculations.

OC-079 FGF19 expression is highly responsive to bile acids compared to other bile acid regulatory genes within the human ileum

IntroductionThe expression of the enteric hormone FGF15 is largely restricted to the ileum in the mouse. FGF15 has also been shown to be the most BA responsive gene in mouse...

Biomimetic Matrices Self-Initiating the Induction of Bone Formation

The new strategy of tissue engineering, and regenerative medicine at large, is to construct biomimetic matrices to mimic nature's hierarchical structural assemblages and mechanisms of simplicity and elegance that are conserved throughout genera and species. There is a direct spatial and temporal relationship of morphologic and molecular events that emphasize the biomimetism of the remodeling cycles of the osteonic corticocancellous bone versus the "geometric induction of bone formation," that is, the induction of bone by "smart" concavities assembled in biomimetic matrices of macroporous calcium phosphate-based constructs. The basic multicellular unit of the corticocancellous bone excavates a trench across the bone surface, leaving in its wake a hemiosteon rather than an osteon, that is, a trench with cross-sectional geometric cues of concavities after cyclic episodes of osteoclastogenesis, eventually leading to osteogenesis. The concavities per se are geometric regulators of growth-inducing angiogenesis and osteogenesis as in the remodeling processes of the corticocancellous bone. The concavities act as a powerful geometric attractant for myoblastic/myoendothelial and/or endothelial/pericytic stem cells, which differentiate into bone-forming cells. The lacunae, pits, and concavities cut by osteoclastogenesis within the biomimetic matrices are the driving morphogenetic cues that induce bone formation in a continuum of sequential phases of resorption/dissolution and formation. To induce the cascade of bone differentiation, the soluble osteogenic molecular signals of the transforming growth factor β supergene family must be reconstituted with an insoluble signal or substratum that triggers the bone differentiation cascade. By carving a series of repetitive concavities into solid and/or macroporous biomimetic matrices of highly crystalline hydroxyapatite or biphasic hydroxyapatite/β-tricalcium phosphate, we were able to embed smart biologic functions within intelligent scaffolds for tissue engineering of bone. The concavities assembled in the bioceramic constructs biomimetize the remodeling cycle of the corticocancellous bone and are endowed with multifunctional pleiotropic self-assembly capacities, initiating angiogenesis and bone formation by induction without the exogenous applications of the osteogenic-soluble molecular signals of the transforming growth factor β supergene family. The incorporation of specific biologic activities into biomimetic matrices by manipulating the geometry of the substratum, defined as geometric induction of bone formation, is now helping to engineer therapeutic osteogenesis in clinical contexts.

On cuspidal representations of general linear groups over discrete valuation rings

We define a new notion of cuspidality for representations of $\GL_n$ over a finite quotient $\Oh_k$ of the ring of integers $\Oh$ of a non-Archimedean local field $F$ using geometric and infinitesimal induction functors, which involve automorphism groups $G_\lambda$ of torsion $\Oh$\nobreakdash-modules. When $n$ is a prime, we show that this notion of cuspidality is equivalent to strong cuspidality, which arises in the construction of supercuspidal representations of $\GL_n(F)$. We show that strongly cuspidal representations share many features of cuspidal representations of finite general linear groups. In the function field case, we show that the construction of the representations of $\GL_n(\Oh_k)$ for $k\geq 2$ for all $n$ is equivalent to the construction of the representations of all the groups $G_\lambda$. A functional equation for zeta functions for representations of $\GL_n(\Oh_k)$ is established for representations which are not contained in an infinitesimally induced representation. All the cuspidal representations for $\GL_4(\Oh_2)$ are constructed. Not all these representations are strongly cuspidal.

Higher regularity of invariant manifolds for nonautonomous equations

For semiflows generated by ordinary differential equations v′ = A(t)v admitting a nonuniform exponential dichotomy, we show that for any sufficiently small perturbation f(t,v) of class Cm, there exist Cm stable and unstable invariant manifolds for the perturbed equation v′ = A(t)v + f(t,v). We emphasize that we do not need to assume the existence of a uniform exponential dichotomy. Our proof of the smoothness of the invariant manifolds is based on a geometric induction argument by considering a linear extension of the vector field, which in particular avoids any lengthy computation related to the higher order derivatives and the induction process. As a consequence, we obtain, in a direct manner, not only the exponential decay of solutions along the stable manifolds but also of their derivatives.

The specification of data parallel algorithms

Several algorithms that illustrate fundamental data parallel operations and the implementation of virtual topologies in terms of hypercube operations are given. A geometric induction principle is developed and used for proving the correctness of these algorithms. The algorithms show how an elementary SIMD language can be used to formally specify and verify data parallel algorithms.

Inequalities for Inscribed and Circumscribed Polygons

In this note, we elaborate on Theorem III. Although it is not stated explicitly in the theorem, it is tacitly assumed from the context that the two polygons are convex and that the center of the circle lies in the interior of both polygons. Uspensky's proof is a nice illustration of induction in geometry, which is not too prevalent (for other examples of geometric induction, see [1]). The inductive step appears in the proof of Theorem I where he first considers the case when angles a and /8 are commensurable so that a =pO and /3 = q3 where p and q are relatively prime integers. It is then supposed that the above inequalities are valid in every case when the sum p + q is less than a given integer N.> 2, from which it is shown to hold forp + q = N. Then the incommensurable case is reduced to the former case by a limiting process. The proof here of Theorem III will be based on the convexity of sinx, which also leads to further related results. Let the central angles subtended by the sides of 6P and 6' from the center of the circle be denoted by 01,02, Om and 9', 02x' ... ,On,f respectively. Uspensky assumes that 0 <Os, O' < -r, and