Some Characterizations of Upper and Lower M-Asymmetric Preirresolute Multifunctions

In this present paper, we introduce and investigate a new form of mappings namely;upper and lower M-asymmetric preirresolute multifunctions defined between M-structural asymmetric topological spaces. The relationships between the multifunctions in our sense and other types of precountinuous and preirresolute multifunctions defined on both symmetric and asymmetric topological structures are discussed.

Upper and Lower Solutions for Impulsive Differential Equations with Application to ODE

In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one solution for the problem. As an application, these results are applied to PBVP of ODE and some examples are given to illustrate our results.

The Estimation for Lower Bounds of the Solutions of Fermat's Equation

Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.

Characteristics and discovery significance of the Upper Triassic–Lower Jurassic marine shale oil in Qiangtang Basin,China

Mesozoic marine shale oil was found in the Qiangtang Basin by a large number of hydrocarbon geological surveys and shallow drilling sampling.Based on systematic observation and experimental analysis of outcrop and core samples,the deposition and development conditions and characteristics of marine shale are revealed,the geochemical and reservoir characteristics of marine shale are evaluated,and the layers of marine shale oil in the Mesozoic are determined.The following geological understandings are obtained.First,there are two sets of marine organic-rich shales,the Lower Jurassic Quse Formation and the Upper Triassic Bagong Formation,in the Qiangtang Basin.They are mainly composed of laminated shale with massive mudstone.The laminated organic-rich shale of the Quse Formation is located in the lower part of the stratum,with a thickness of 50–75 m,and mainly distributed in southern Qiangtang Basin and the central-west of northern Qiangtang Basin.The laminated organic-rich shale of the Bagong Formation is located in the middle of the stratum,with a thickness of 250–350 m,and distributed in both northern and southern Qiangtang Basin.Second,the two sets of laminated organic-rich shales develop foliation,and various types of micropores and microfractures.The average content of brittle minerals is 70%,implying a high fracturability.The average porosity is 5.89%,indicating good reservoir physical properties to the level of moderate–good shale oil reservoirs.Third,the organic-rich shale of the Quse Formation contains organic matters of types II1 and II2,with the average TOC of 8.34%,the average content of chloroform bitumen'A'of 0.66%,the average residual hydrocarbon generation potential(S1+S2)of 29.93 mg/g,and the Ro value of 0.9%–1.3%,meeting the standard of high-quality source rock.The organic-rich shale of the Bagong Formation contains mixed organic matters,with the TOC of 0.65%–3.10%and the Ro value of 1.17%–1.59%,meeting the standard of moderate source rock.Fourth,four shallow wells(depth of 50–250 m)with oil shows have been found in the organic shales at 50–90 m in the lower part of the Bagong Formation and 30–75 m in the middle part of the Quse Formation.The crude oil contains a high content of saturated hydrocarbon.Analysis and testing of outcrop and shallow well samples confirm the presence of marine shale oil in the Bagong Formation and the Quse Formation.Good shale oil intervals in the Bagong Formation are observed in layers 18–20 in the lower part of the section,where the shales with(S0+S1)higher than 1 mg/g are 206.7 m thick,with the maximum and average(S0+S1)of 1.92 mg/g and 1.81 mg/g,respectively.Good shale oil intervals in the Quse Formation are found in layers 4–8 in the lower part of the section,where the shales with(S0+S1)higher than 1 mg/g are 58.8 m thick,with the maximum and average(S0+S1)of 6.46 mg/g and 2.23 mg/g,respectively.

A PRIORI ESTIMATE FOR LOWER SOLUTIONS OF ACLASS QUASILINEAR ELLIPTIC EQUATIONS

A new priori estimate of lower- solution is made for the following quasilinear elliptic equation : integral(G) {del v . A (x, u, del u) + vB (x, u, del u)} dx = 0, For All v is an element of (W) over circle(p)(1) (G). The result presented in this paper enriches and extends the corresponding result of Gilbarg-Trudinger.

Upper Bound Solutions for Uplift Ultimate Bearing Capacity of Suction Caisson Foundation

Suction caisson foundation derives most of their uplift resistance from passive suction developed during the pullout movement. It was observed that the passive suction generated in soil at the bottom of the caisson and the failure mode of suction caisson foundation subjecting pullout loading behaves as a reverse compression failure mechanism.The upper bound theorems have been proved to be a powerful method to find the critical failure mechanism and critical load associated with foundations, buried caissons and other geotechnical structures. However, limited attempts have been reported to estimate the uplift bearing capacity of the suction caisson foundation using the upper bound solution. In this paper, both reverse failure mechanisms from Prandtl and Hill were adopted as the failure mechanisms for the computation of the uplift bearing capacity of the suction caisson. New equations were proposed based on both failure mechanisms to estimate the pullout capacity of the suction caisson. The proposed equations were verified by the test results and experimental data from published literature. And the two solutions agree reasonably well with the other test results. It can be proved that both failure mechanisms are reasonably and more consistent with the actual force condition.

A Generalized Upper and Lower Solution Method for Singular Discrete Boundary Value Problems

This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.

About Upper and Lower Strong Fractional Weighted Mean Convergence by Moduli for Triple Sequences

In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f, I established that a triple sequence that is f-upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f-lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains.

Some Results of Upper and Lower <i>M</i>-Asymmetric Irresolute Multifunctions in Bitopological Spaces

In this paper, we aim to introduce and study some basic properties of upper and lower M-asymmetric irresolute multifunctions defined between asymmetric sets in the realm of bitopological spaces with certain minimal structures as a generalization of irresolute functions deal to Crossley and Hildebrand [1] and upper and lower irresolute Multifunctions deal to Popa [2].

Enrichment model and major controlling factors of below-source tight oil in Lower Cretaceous Fuyu reservoirs in northern Songliao Basin,NE China

Based on the geochemical,seismic,logging and drilling data,the Fuyu reservoirs of the Lower Cretaceous Quantou Formation in northern Songliao Basin are systematically studied in terms of the geological characteristics,the tight oil enrichment model and its major controlling factors.First,the Quantou Formation is overlaid by high-quality source rocks of the Upper Cretaceous Qingshankou Formation,with the development of nose structure around sag and the broad and continuous distribution of sand bodies.The reservoirs are tight on the whole.Second,the configuration of multiple elements,such as high-quality source rocks,reservoir rocks,fault,overpressure and structure,controls the tight oil enrichment in the Fuyu reservoirs.The source-reservoir combination controls the tight oil distribution pattern.The pressure difference between source and reservoir drives the charging of tight oil.The fault-sandbody transport system determines the migration and accumulation of oil and gas.The positive structure is the favorable place for tight oil enrichment,and the fault-horst zone is the key part of syncline area for tight oil exploration.Third,based on the source-reservoir relationship,transport mode,accumulation dynamics and other elements,three tight oil enrichment models are recognized in the Fuyu reservoirs:(1)vertical or lateral migration of hydrocarbon from source rocks to adjacent reservoir rocks,that is,driven by overpressure,hydrocarbon generated is migrated vertically or laterally to and accumulates in the adjacent reservoir rocks;(2)transport of hydrocarbon through faults between separated source and reservoirs,that is,driven by overpressure,hydrocarbon migrates downward through faults to the sandbodies that are separated from the source rocks;and(3)migration of hydrocarbon through faults and sandbodies between separated source and reservoirs,that is,driven by overpressure,hydrocarbon migrates downwards through faults to the reservoir rocks that are separated from the source rocks,and then migrates laterally through sandbodies.Fourth,the differences in oil source conditions,charging drive,fault distribution,sandbody and reservoir physical properties cause the differential enrichment of tight oil in the Fuyu reservoirs.Comprehensive analysis suggests that the Fuyu reservoir in the Qijia-Gulong Sag has good conditions for tight oil enrichment and has been less explored,and it is an important new zone for tight oil exploration in the future.

Upper and Lower Semicontinuity of Solution Sets for Parametric Generalized Vector Quasi-equilibrium Problems

In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.

Ground State Solutions for a Kind of Schrödinger-Poisson System with Upper Critical Exponential Convolution Term

This paper mainly discusses the following equation: where the potential function V : R3 → R, α ∈ (0,3), λ > 0 is a parameter and Iα is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.

Existence of Solutions for S-L Singular Boundary Value Problems with p-Laplacian Operators

The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map.

Existence of Positive Solutions for a Class of Degenerate and Nondegenerate Stable Diffusion Models

This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.

A Combination of N2 and CO2 Adsorption to Characterize Nanopore Structure of Organic-Rich Lower Silurian Shale in the Upper Yangtze Platform, South China： Implications for Shale Gas Sorption Capacity

The pores in shales are mainly of nanometer-scale, and their pore size distribution is very important for the preservation and exploitation of shale gas. This study focused on the organic-rich Lower Silurian black shale from four wells in the Upper Yangtze Platform, and their TOC, mineralogical composition and pore characterization were investigated. Low pressure N2 and CO2 adsorption were conducted at 77.35 K and 273.15 K, respectively, and the pore structures were characterized by modified Brunauer-Emmett-Teller （BET）, Dubinin-Radushkevich （DR）, t-plot, Barrett- Joyner-Halenda （BJH） and density functional theory （DFT） methods and then the relationship between pore structure and shale gas sorption capacity was discussed. The results indicate that （1） The Lower Silurian shale has high TOC content of 0.92%~96%, high quartz content of 30.6%-69.5%, and high clays content of 24.1%-51.2%. The total specific surface area varies from 7.56 m^2/g to 25.86 m^2/g. Both the total specific surface area and quartz content are positively associated with the TOC content. （2） Shale samples with higher TOC content have more micropores, which results in more complex nanopore structure. Micropore volumes/surface areas and non-micropore surface areas all increase with the increasing TOC content. （3） A combination of N2 and CO2 adsorption provides the most suitable detection range （~0.3-60 nm） and has high reliability and accuracy for nanopore structure characterization. （4） The TOC content is the key factor to control the gas sorption capacity of the Lower Silurian shale in the Upper Yangtze Platform.

Upper Devonian and Lower Carboniferous Sequence Stratigraphy of South China

In South China four depositional sequences are recognized in the upper part of Upper Devonian and Tournaisian. They are named SQ0 SQ1, SQ2 and SQ3 in ascending order. SQ0 is Strunian (uppermost Devonian), and the other three Tournaisian in age. These four depositional sequences appear to correlate fairly well with the four sequence recognized in Europe, North America and other areas. This may suggest that these sequences are synchronous depos- its resulted from the eustatic changes. The present study on sequence stratigraphy, biostratigraphy and event stratigraphy indicates that in neritic facies areas of South China, the Devonian-Carboniferous boundary, matching the boundary between Siphonodella praesulcata zone and S. sulcata zone in pelagic facies areas, is not only higher than the top of the Cystophrentis zone, but also higher than the top of the Devonian-Carboniferous boundary event bed. In neritic facies areas, the Devonian-Carbonifrerous boundary is marked by the most distinct transgressive surface within the Cystophrentiseudouralina interval zone, i. e. at the base of the TST of the SQ1. This boundary coincides with the top surface of the event bed resulted from the eustatic fall, and approximately corresponds to the basal part of Rseudouralina assemblage zone.

Ramp facies in an intracratonic basin:A case study from the Upper Devonian and Lower Carboniferous in central Hunan,southern China

Detailed studies on Late Devonian to Early Carboniferous carbonate rocks in central Hunan, southern China have led to the recognition of 25 lithofacies which can be grouped into： （I） inner ramp peritidal platform, （2） inner ramp organic hank and mound, （3） mid ramp, （4） outer ramp, and （5） shelf basin facies associations. The peritidal platform facies association dominates the Zimenqiao Formation （Namurian A or late Datangian） and is characterized by gypsum and dolostone-containing sequences, indicating a peritidal platform environment. The other four facies associations dominate the Menggongao Formation （late Famennian）, Liujiatang Formation （Tournaisian or Yangruanian）, Shidengzi Formations （early Visean or early Datangian）. Five upward-shallowing cycles were distinguished in these three Formations. The predominant facies associations developed in each Formation demonstrate an overall transgression-regression cycle in the Late Devonian to Early Carboniferous in central Hunan. The overall transgressive sequence was preserved in the Shaodong, Menggongao, and Liujiatang Formations, and the overall regressive sequence was preserved in the Liujiatang, Shidengzi, Ceshui and Zimenqiao Formations.

Controls on the organic carbon content of the lower Cambrian black shale in the southeastern margin of Upper Yangtze

Control of various factors, including mineral components, primary productivity and redox level, on the total organic carbon(TOC) in the lower Cambrian black shale from southeastern margin of Upper Yangtze(Taozichong, Longbizui and Yanbei areas) is discussed in detail in this article. Mineral components in the study strata are dominated by quartz and clay minerals. Quartz in the Niutitang Formation is mainly of biogenic origin, and the content is in positive correlation with TOC, while the content of clay minerals is negatively correlated with TOC. Primary productivity, represented by the content of Mobio(biogenic molybdenum), Babio(biogenic barium) and phosphorus, is positively correlated with TOC. The main alkanes in studied samples are nCC, and odd–even priority values are closed to 1(0.73–1.13), which suggest the organic matter source was marine plankton. Element content ratios of U/Th and Ni/Co and compound ratio Pr/Ph indicate dysoxic–anoxic bottom water, with weak positive relative with TOC. In total, three main points can be drawn to explain the relationship between data and the factors affecting organic accumulation:(1) quartz-rich and clay-mineral-poor deep shelf–slope–basin environment was favorable for living organisms;(2) high productivity provided the material foundation for organic generation;(3) the redox conditions impact slightly on the content of organic matter under high productivity and dysoxic–anoxic condition.

Differences of Hydrocarbon Enrichment between the Upper and the Lower Structural Layers in the Tazhong Paleouplift

The Tazhong paleouplift is divided into the upper and the lower structural layers, bounded by the unconformity surface at the top of the Ordovician carbonate rock. The reservoirs in the two layers from different parts vary in number, type and reserves, but the mechanism was rarely researched before. Therefore, an explanation of the mechanism will promote petroleum exploration in Tazhong paleouplift. After studying the evolution and reservoir distribution of the Tazhong paleouplift, it is concluded that the evolution in late Caledonian, late Hercynian and Himalayan periods resulted in the upper and the lower structural layers. It is also defined that in the upper structural layer, structural and stratigraphic overlap reservoirs are developed at the top and the upper part of the paleouplift, which are dominated by oil reservoirs, while for the lower structural layer, lithological reservoirs are developed in the lower part of the paleouplift, which are dominated by gas reservoirs, and more reserves are discovered in the lower structural layer than the upper. Through a comparative analysis of accumulation conditions of the upper and the lower structural layers, the mechanism of enrichment differences is clearly explained. The reservoir and seal conditions of the lower structural layer are better than those of the upper layer, which is the reason why more reservoirs have been found in the former. The differences in the carrier system types, trap types and charging periods between the upper and the lower structural layers lead to differences in the reservoir types and distribution. An accumulation model is established for the Tazhong paleouplift. For the upper structural layer, the structural reservoirs and the stratigraphic overlap reservoirs are formed at the upper part of the paleouplift, while for the lower structural layer, the weathering crust reservoirs are formed at the top, the reef-flat reservoirs are formed on the lateral margin, the karst and inside reservoirs are formed in the lower part of the paleouplift.

On the upper bounds of (1,0)-super solutions for the regular balanced random (k,2s)-SAT problem

This paper explores the conditions which make a regular balancedrandom(k,2s)-CNFformula(1,O)-unsatisfiable with high probability.The conditions also make a random instance of the regular balanced(k-1,2(k-1)s)-SAT problem unsatisfiable with high probability,where the instance obeys a distribution which differs from the distribution obeyed by a regular balanced random(k-1,2(k-1)s)-CNF formula.Let F be a regular balanced random(k,2s)-CNF formula where k≥3,then there exists a number so such that F is(1,O)-unsatisfiable with high probability if s>so.A numerical solution of the number so when k e(5,6,...,14)is given to conduct simulated experiments.The simulated experiments verify the theoretical result.Besides,the experiments also suggest that F is(1,O)-satisfiable with high probability if s is less than a certain value.