Topological Analysis of Fibrations in Multidimensional (C, R) Space

A holomorphically fibred space generates locally trivial bundles with positive dimensional fibers. This paper proposes two varieties of fibrations (compact and non-compact) in the non-uniformly scalable quasinormed topological (C, R) space admitting cylindrically symmetric continuous functions. The projective base space is dense, containing a complex plane, and the corresponding surjective fiber projection on the base space can be fixed at any point on real subspace. The contact category fibers support multiple oriented singularities of piecewise continuous functions within the topological space. A composite algebraic operation comprised of continuous linear translation and arithmetic addition generates an associative magma in the non-compact fiber space. The finite translation is continuous on complex planar subspace under non-compact projection. Interestingly, the associative magma resists transforming into a monoid due to the non-commutativity of composite algebraic operation. However, an additive group algebraic structure can be admitted in the fiber space if the fibration is a non-compact variety. Moreover, the projection on base space supports additive group structure, if and only if the planar base space passes through the real origin of the topological (C, R) space. The topological analysis shows that outward deformation retraction is not admissible within the dense topological fiber space. The comparative analysis of the proposed fiber space with respect to Minkowski space and Seifert fiber space illustrates that the group algebraic structures in each fiber spaces are of different varieties. The proposed topological fiber bundles are rigid, preserving sigma-sections as compared to the fiber bundles on manifolds.

A Note on the $$L^p$$ Integrability of a Class of Bochner–Riesz Kernels

For a general compact variety $$\Gamma $$ Γ of arbitrary codimension, one can consider the $$L^p$$ L p mapping properties of the Bochner–Riesz multiplier $$\begin{aligned} m_{\Gamma , \alpha }(\zeta ) \ = \ \mathrm{dist}(\zeta , \Gamma )^{\alpha } \phi (\zeta ) \end{aligned}$$ m Γ , α ( ζ ) = dist ( ζ , Γ ) α ϕ ( ζ ) where $$\alpha > 0$$ α > 0 and $$\phi $$ ϕ is an appropriate smooth cutoff function. Even for the sphere $$\Gamma = {{\mathbb {S}}}^{N-1}$$ Γ = S N - 1 , the exact $$L^p$$ L p boundedness range remains a central open problem in Euclidean harmonic analysis. In this paper we consider the $$L^p$$ L p integrability of the Bochner–Riesz convolution kernel for a particular class of varieties (of any codimension). For a subclass of these varieties the range of $$L^p$$ L p integrability of the kernels differs substantially from the $$L^p$$ L p boundedness range of the corresponding Bochner–Riesz multiplier operator.

Agronomic Behavior of Six Saladette Tomato Hybrids Grown under Shade Mesh

Aims: The objective was to evaluate six indeterminate saladette tomato hybrids in Southeast, Coahuila, Mexico. Under shade house covered with anti-aphid mesh, to determine their performance, commercial quality and adaptability. Study Design: The experimental design used in each test was completely randomized model with six treatments and three repetitions each. The treatments were hybrids Lubino were Lubino F1, Zopilote F1, Sahariana F1, Raptor F1, Quetzal F1 and RTF-713172 F1. Place and Duration of Study: The site was Parras Valley Tomatoes in Parras, Coahuila, México. During april to November 2017. Methodology: The distance between the lines were 1.80 m, between the plantpots 36 cm and two plants per plantpots, with approximately 30,000 plants per hectare calculated. The genotypes used were Lubino F1, Zopilote F1, Sahariana F1, Raptor F1, Quetzal F1 and RTF-713172 F1. The following agronomic characteristics were evaluates: yield, total number of fruits, average fruit weight, number of fruits per bunch, length between clusters, length of internodes, main stem thickness and commercial quality of fruit. Results: The results indicate that the highest yielding hybrid was Zopilote with 4.3 kg plant-1, followed by Saharan, the average weight of the product obtained best in Saharan and Quetzal with 122.33 and 118.33 g respectively, the most compact variety was Zopilote due to the shorter distance between bunches, contrary to what was demonstrated by Lubino. Conclusion: The best variety for the Southeast of Coahuila is Zopilote F1, due to its higher yield and for being a compact plant.

The impact of calcination on changes in the physical and mechanical properties of the diatomites of the Leszczawka Member (the Outer Carpathians, Poland)

The work concerned the effects of the thermal treatment of diatomites from the Jawornik deposit (an example of the diatomites of the Leszczawka Member of the Polish Outer Carpathians). Five distinct lithological varieties were subjected to calcination at 600°C in ambient air.The thermal impact induced the following changes to the rocks. Their overall rock porosity increased, most distinctly in the initially softer varieties, and the internal pores of the siliceous frustules themselves usually became larger due to the initial melting of the silica phases. Most of the diatoms, quartz and feldspars cracked as a result of their brittle fracturing under compressive strain resulting from substantial and differing size changes of growing grains. Clay minerals were thermally transferred, changing their volume. The organic matter dispersed through-out the diatomites was partly oxidized and removed. At the same time, the structure of the rocks was strengthened, as confirmed by an increase in their microhardness. The microhardness of soft and porous diatomite varieties increased considerably on heating, but that of the hard and compact variety changed to a smaller degree. The increase is directly related to the content of the clay minerals. The impact of other mineral components was not detected. The calcination of lithologically diversified diatomites provided the mineral with raw material with deicing and antisliding properties. The technology of its production has been determined by the authors and submitted as a patent.

KNOTTING OF REGULAR POLYGONS IN 3-SPACE

The probability that a linear embedding of a regular polygon in R3 is knotted should increase as a function of the number of sides. This assertion is investigated by means of an exploration of the compact variety of based oriented linear maps of regular polygons into R3. Asymptotically, an estimation of the probability of knotting is made by means of the HOMFLY polynomial.