MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Characteristics and influencing mechanisms of production-living-ecological space dynamics in the Three Gorges Reservoir Area(TGRA),Chongqing,China

The Three Gorges Reservoir Area(TGRA)is an important ecological barrier in the Yangtze River Basin,China.Therefore,it is of great importance to understand the spatio-temporal variation and the driving factors of production-living-ecological spaces for sustainable and high-quality development in the TGRA.This study investigated the dynamic variation of production-living-ecological spaces in the TGRA by employing land use data in 2000,2005,2010,2015,and 2018,and detected the influencing factors by using the Geographic detector(GeoDetector).Results implied that the structure and dynamic trajectories of production-living-ecological spaces in the TGRA varied in both horizontal and vertical directions,and the study area was dominated by ecological space.A spatial orientation towards the northeast was detected in the evolution of production-living-ecological spaces during 2000-2018.In terms of quantity,the transition from ecological space(grassland and woodland)to agriculture land accounted for the largest proportion from 2000 to 2018.However,the reverse transition from agriculture land to ecological space has increased since 2000 with the efforts of“Grain for Green”.In terms of temporal scale,there was a fluctuating trend in production space with the continuous expansion of living space,while ecological space showed an inverted U-shaped trend during 2000-2018.The dynamic pattern of production-living-ecological spaces in the TGRA was influenced by both physical and socio-economic variables as basic determinants and dominant driving factors,respectively.Finally,the harmonization and protection of production-living-ecological spaces still require policy-makers’efforts.This work may have potential in advancing our understanding about land use conflicts,and provide a reference for rational layout of spatial functions and the realization of sustainable development in the TGRA.

Butterfly taxonomic and functional diversity in the urban green spaces of Hefei city

Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study aimed to investigate the community composition characteristics of butterflies in urban green spaces within the context of rapid urbanization. Simultaneously, it explored the status and differences in butterfly taxonomic diversity, functional diversity, and functional traits among different types of urban green spaces, regions, and urban gradients to provide relevant insights for further improving urban green space quality and promoting biodiversity conservation. We conducted a year-long survey of 80 green spaces across different urban regions and ring roads within Hefei City, Anhui Province, with monthly sampling intervals over 187 transects. A total of 4822 butterflies, belonging to 5 families, 17 subfamilies, 40 genera, and 55 species were identified. The species richness, Shannon, Simpson, functional richness, and Rao's quadratic entropy indices of butterflies in urban park green spaces were all significantly higher than those in residential and street green spaces(P < 0.05). Differences in butterfly diversity and functional traits among different urban regions and ring roads were relatively minor, and small-sized, multivoltine, and long flying duration butterflies dominated urban green spaces. Overall, these spaces offer more favorable habitats for butterflies. However, some residential green spaces and street green spaces demonstrate potential for butterfly conservation.

Integrity and Size of Green Spaces Are Critical for the Functional Di-versity of Birds:Evidence from the Eastern and Northwestern Regions of China

Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple datasets to explore the effects of land-scape patterns and natural environments on the functional diversity of birds in urban parks and campuses in the eastern and northwest-ern regions of China.Firstly,we used the data to calculate birds of the functional richness(FRic),functional evenness(FEve),and func-tional divergence(FDiv)of 68 urban spaces in the eastern and northwestern regions of China.Further,we established generalized linear models of natural factors,human factors,and functional diversity.Results showed more bird species with unique traits were in the north-western region.This may be because the earlier urbanization in the eastern region filtered out urban-sensitive species,leaving behind urban adapters.Moreover,we found that the fractal dimension index was the most significant positive factor of FRic in the eastern re-gion but the most significant negative factor of FDiv.Elevation was the most significant negative influence factor of FEve in the eastern region,but it was the most potent positive influence factor of FRic in the northwestern region.Population density had a significant posit-ive effect on FDiv in the northwestern region.However,green space areas significantly negatively impacted FEve in the northwestern region.In addition,birds in parks in both regions had more functional traits than those on campuses,possibly because of the larger green space in parks,which may contain more fragments of native vegetation and reduce human interference.Our study suggests that pre-serving more original vegetation and reducing human disturbance in cities can increase the functional diversity of urban birds and im-prove urban ecosystem functions.

Evaluation of the production-living-ecology space function suitability of Pingshan County in the Taihang mountainous area,China

A rational utilization of land is a matter of importance in sustainable development of mountainous area.The land function in mountainous areas has a close connection with space structure of ecology,production and living.To promote a harmonious development of the relationship between people and nature in mountainous areas,it is necessary to coordinate their relationships of space functions.Suitability evaluation of basic unit function associated with multi-scale space analysis is a prerequisite to a reasonable optimization of land function structure.In this study,an optimized evaluation index system of combination functions was introduced into the assessment of ecological spatial functional suitability in ecological fragile regions by adding three indicators,namely,soil erosion sensitivity,landscape ecological risk and ecological sensitivity.The principle of"taking high"(referred to a function with high suitability to be regarded as the main function of an evaluation unit)and ecological priority(referred to the case,supposing the suitability of a unit’s three functions is consistent,the main function is determined to be the ecological function)were used to determine the main function of an evaluation unit.Pingshan County,China,located at the eastern foot of the Taihang Mountain,was targeted in this case study.The production-livingecology space(PLES)function in Pingshan was identified by applying our improved valuation indexes.Further,the functional suitability distribution of the combination of elements was obtained by using overlapping comprehensive analysis method,considering the tradeoff of the functional suitability of combination elements.The regions suitable for production/living were distributed in relatively flat piedmont plains,whereas the regions suitable for ecology were distributed in the mountain areas of middle and low altitudes.Therefore,to maintain a sustainable development in mountainous areas,an improved scheme of development for Pingshan should be to delineate ecologically fragile areas,to build ecological industrial parks near existing scenic spots,to protect basic agricultural production areas,and to increase investment in science and technology,including reasonable ecological compensation.This study can provide reference for the planning of sustainable development in the Taihang Mountain area and similar regions.

Inhomogeneous Besov and Triebel-Lizorkin spaces associated with a para-accretive function and their applications

In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applications,pointwise multiplier theorems are also obtained.

Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.

q–differ-integral operator on p–valent functions associated with operator on Hilbert space

Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

Analysis of the Energy and Environmental Sustainability of a Built Space System: The Case of Patte d’Oie University Campus in Ouagadougou

The aim of this study was to carry out a dynamic simulation of the energy and environmental performance of a built space system, with a view to assessing its energy and environmental class. The use of a simulation and modeling tool, supported by various methodological references, formed the basis of our approach. Adopting a systemic perspective, we described the structural and functional aspects of the systems making up built spaces, as well as the associated energy flows. Our approach was also based on a typology, taking into account typical days, structural and functional configurations at different scales and angles of observation. The analysis tool we developed in Java was applied to the built space system of the Patte d’Oie university campus in Ouagadougou. Annual electricity consumption was measured at 124387.34 kWh, closely aligned with the average annual electricity bill (125224.31 kWh), with a maximum relative deviation of 1%, followed by a carbon emission balance of 58337.66 kg eq CO2 per year. This validation confirmed the effectiveness of our tool. In addition, following the analysis of electricity consumption using our tool, the university campus was classified in energy class B and environmental class C. These results will be based on the emission factors of the energy mix of the West African Economic and Monetary Union (WAEMU) territory, with particular emphasis on Burkina Faso.

High complex anal fistula managed by the modified transanal opening of the intersphincteric space via the inter-sphincteric approach:A case report

BACKGROUND High complex anal fistulas are epithelialized tunnels,with the main fistula piercing above the deep external sphincter and the internal opening approaching the dentate line.Conventional surgical procedures for high complex anal fistulas remove most of the external sphincter and damage the anorectal ring.Postoperative loss of anal function can cause physical and mental damage.Transanal opening of the intersphincteric space(TROPIS)is an effective procedure that completely preserves the external anal sphincter.However,its clinical application is limited by challenges in the localization of the internal opening of a fistula and the high risk of complications.On the basis of our clinical experience,we modified the TROPIS procedure for the treatment of treating high complex anal fistulas.CASE SUMMARY A patient with a high complex anal fistula located above the anorectal ring underwent modified TROPIS,which involved sepsis drainage and identification of the internal opening in the intersphincteric space.The patient with the high complex anal fistula recovered well postoperatively,without any postoperative complications or anal dysfunction.Anal function returned to normal after 17 months of follow-up.CONCLUSION The modified TROPIS procedure is the most minimally invasive surgery for anal fistulas that minimally impairs anal function.It allows the complete removal of infected anal glands and reduces the risk of postoperative complications.Modified TROPIS via the intersphincteric approach is an alternative sphincter-preserving treatment for high complex anal fistulas.

THE BASIC THEORY OF SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH BOUNDED DELAY IN THE SPACE OF INTEGRABLE FUNCTIONS

在可积函数空间中讨论有界滞量泛函微分方程，建立其解的基本理论，包括解的存在性，唯一性及延展性。

Ecological function transitions of land use in the Beibu Gulf Economic Zone from the perspective of production-living-ecological space

The ecological function of land use is the basis for developing an ecological civilization and realizing sustainable development.This paper may help guide the coordination of economic development and ecological development in China’s coastal border areas.Based on theoretical analysis,this paper studies the spatiotemporal evolution of the functional spaces and the ecological function transitions of land use in the Beibu Gulf Economic Zone(BGEZ)by analyzing patterns,processes,and factors by applying eco-environmental quality index,grid subdivision,kriging interpolation,barycenter model,and Geodetector.This paper constructs a theoretical framework of ecological function transitions of land use based on the research idea of“system-pattern-process-factor”,and carries out empirical research.Some conclusions can be drawn as follows:(1)The ecological space in the BGEZ has continuously decreased,converting mainly into agricultural production space and industrial-mining production space.The production space has expanded slowly.The area of living space in the BGEZ has increased rapidly.(2)The ecological function of land use in the BGEZ has continued to weaken,especially in the southern part of the BGEZ.The“high-sub-high”quality zones of ecological function are retreating to the north.(3)There were more deterioration transition areas than optimization transition areas of ecological function in the BGEZ.The former were mostly located in the central and southern urbanized areas of the BGEZ,whereas the latter were mostly located in the edge zones of district and county units.(4)As for the driving factors of the deterioration transitions of land use ecological function in the BGEZ,the significant trend of“de-ecologization”of the land cover/land use structure was the dominant driving factor;the interactions among the“natural-socioeconomic-managerial”systems were the main recessive factor.The natural system played a fundamental role,and the driving force of natural factors was the strongest.The industrialization,urbanization,and GDP increment in the socioeconomic system and the policy positioning of development intensity in the managerial system played a significant role.The interactions among natural factors,road construction,and industrial non-agricultural transformation had a“fuze”effect on stimulating driving forces.

Perirenal space blocking restores gastrointestinal function in patients with severe acute pancreatitis

AIM:To investigate effects of perirenal space blocking(PSB)on gastrointestinal function in patients with severe acute pancreatitis(SAP).METHODS:Forty patients with SAP were randomly allocated to receive PSB or no PSB(NPSB).All the SAP patients received specialized medical therapy(SMT).Patients in the PSB group received PSB+SMT when hospitalized and after diagnosis,whereas patients in the NPSB group only received SMT.A modifed gastrointestinal failure(GIF)scoring system was used to assess the gastrointestinal function in SAP patients after admission.Pain severity(visual analog scale,0 to100)was monitored every 24 h for 72 h.RESULTS:Modified GIF score decreased in both groups during the 10-d study period.The median score decrease was initially significantly greater in the PSB group than in the NPSB group after PSB was per-formed.During the 72-h study period,pain intensity decreased in both groups.The median pain decrease was significantly greater in the PSB group than in the NPSB group at single time points.Patients in the PSB group had significantly lower incidences of hospital mortality,multiple organ dysfunction syndrome,systemic inflammatory response syndrome,and pancreatic infection,and stayed in the intensive care unit for a shorter duration.However,no difference in terms of operation incidence was found between the two groups.CONCLUSION:PSB could ameliorate gastrointestinal dysfunction or failure during the early stage of SAP.Moreover,PSB administration could improve prognosis and decrease the mortality of SAP patients.

ON SOME GENERALIZED DIFFERENCE PARANORMED SEQUENCE SPACES ASSOCIATED WITH MULTIPLIER SEQUENCE DEFINED BY MODULUS FUNCTION

In this article we introduce the paranormed sequence spaces （f,A, Am,p）, c0（f,A,Am,p） and L00（f,A, Am,p）, associated with the multiplier sequence ∧ = （hk）, defined by a modulus function f. We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results.

DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are (weak) Asplund spaces.

Function spaces of Besov-type and Triebel-Lizorkin-type——a survey

This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.

ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

Differentiability of Convex Functions in Locally Convex Spaces（Ⅰ）──Continuous Convex Functions and Gateaux Differentiability

The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important results for this research area in locally convex spaces.

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHRDINGER OPERATORS

In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.