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The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: P t = P 0 e x p ± t / τ β , and SM-2 is the Malthus-type relation with the time-dependent growth rate r (t) or relaxation time τ (t) = 1 / r (t) : P t = P 0 e x p r t × t = P 0 e x p τ t / t . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ( β > 1) to the stretched exponential one ( β < 1 ). For SM-2 dependence, linear changes of τ T during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior P t = P 0 e x p b ′ t / T C - t , where T C ≈ 2216 is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis. [ABSTRACT FROM AUTHOR]

In the context of the separation of three rights of land and agricultural modernization, this paper is based on the land economic survey data from eleven provinces in China in 2019, covering the eastern, middle, and western regions of China. Based on the value chain theory and its "second-round effect", which pertains to the multi-round effects of value chain distribution theory, various research methods such as Probit, Tobit, the two-part model, SFA, PSM, and the intermediary effect model are employed to analyze the direct impact of the agriculture value chain (AVC) on farmers' land factor inputs and the income effects caused by them, which are the "second-round effect" of the AVC on land factor inputs. The research results show the following: Firstly, the AVC has a significant positive impact on the behavior and area of farmers' land transferring-in, which helps guide farmers towards large-scale land operation. Secondly, the AVC significantly improves farmers' production efficiency and promotes land transfer through differences in production efficiency, representing the "second-round effect" mechanism of the AVC on land factor inputs. Moreover, the AVC will increase farmers' net land production income by 48.74%, which is the "second-round effect" of the AVC on farmers' agricultural income and also the motivation for farmers' land factor inputs. Finally, the expansion of land area and the improvement of production efficiency jointly increase farmers' agricultural income, among which production efficiency plays a partial intermediary effect in increasing agricultural income if farmers join the AVC. This paper believes that we should further promote the market-oriented reform of land factors, support the innovation of the benefit linkage mechanism of the AVC, and promote appropriate areas of land operation by farmers, thereby achieving common prosperity and promoting agricultural modernization in China. [ABSTRACT FROM AUTHOR]

The authors address the complex oscillation problems of all solutions of homogenous linear differential equations with meromorphic coefficients. Sufficient conditions for estimating the growth of meromorphic solution with infinite order have been proposed based on Nevanlinna value distribution theory. Compared with the existing results, the proposed hyper-order of all meromorphic solutions with infinite order can be estimated in terms of a bounded interval which includes information of order of growth of meromorphic functions and meromorphic polynomial coefficients. [ABSTRACT FROM AUTHOR]

In the value distribution theory of complex analysis, Petrenko's deviation is to describe more precisely the quantitative relationship between T(r, f) and log M(r, f) when the modulus of variable |z| = r is sufficiently large. In this paper we introduce Petrenko's deviations to the coefficients of three types of complex equations, which include difference equations, differential equations and differential-difference equations. Under different assumptions we study the lower bound of limiting directions of Julia sets of solutions of these equations, where Julia set is an important concept in complex dynamical systems. The results of this article show that the lower bound of limiting directions mentioned above is closely related to Petrenko's deviation, and our conclusions improve some known results. [ABSTRACT FROM AUTHOR]

Our goal in this paper is to establish some second main theorems for holomorphic mappings from angular domains into projective varieties intersecting arbitrary families of moving hypersurfaces with truncated counting functions. Our results generalize and also improve all previous results for the case of holomorphic mappings from the complex plane. [ABSTRACT FROM AUTHOR]

In Nevanlinna's value distribution theory we considering some basic terms like T (r, f), N (r, f), m(r, f) etc., and let f m(z) + q(z)[f nΔqηf ](k) = p(z) be a non-linear q-th order difference equation and f (z) be a transcendental meromorphic function with finite order m, n and k be a positive integers such that m ≥ (q + 1)(nk + k + 2) + 3, p(z) be a meromorphic function satisfying N-r, pZ) = S(r, f)∙ The q(z) be a non-zero meromorphic function satisfying that T(r, q(z)) = S(r, f), then f(z) is not a solution of the non-linear q-th order difference equation. In this paper, we mainly investigate the uniqueness result of transcendental Fermat type q-shift equation by considering q-th order difference equation. Our result improves the results due to Abhijit Banerjee and Tania Biswas. In addition to that the example is exhibited to validate certain claims and justification of our main result. [ABSTRACT FROM AUTHOR]

Some fundamental terms in Nevanlinna's value distribution theory m(r, f), N(r, f), T(r, f), etc. and let f(z) and g(z) be two non-constant meomorphic functions, P(f) and P(g) be a polynomials of degree m, whose zeros and poles are of multiplicities atleast s, where s is a positive integer, and let n, k be two positive integers with s(n + m) > 9k + 14. If m ≥ 2 and ..., if m = 1 and ... and [gnP(g)](k) share 1(1, 0), then either [fnP(f)](k)[gnP(g)](k) = 1 or f(z) and g(z) satisfy the algebraic equation R(f, g) = 0, where .... Let f(z) and g(z) be two non-constant entire functions with satisfying inequality n > 5k + 6m + 7. The present paper deals with the study of uniqueness of certain differential polynomials with the notion of weighted sharing. The results of the paper improve and generalize the results of Rajeshwari S, Husna V and Nagarjun V [6]. We have also exhibited a series of examples satisfying our results and provided some other examples showing the sharpness of one of our results. [ABSTRACT FROM AUTHOR]

The study considers the inverse problem in the scattering theory in one-dimensional Schrödinger equation. The corresponding scattering matrix consists of 2 × 2 entries of meromorphic functions. We are interested to recover the potential source from certain information of the quotients of scattering coefficients that is known a priori. [ABSTRACT FROM AUTHOR]

In this paper, by using the Nevanlinna value distribution theory of meromorphic functions on an annulus, we deal with the growth properties of solutions of the linear differential equation f(k)+Bk-1 (z) f(k-1)+· · ·+B¹ (z) f'+B0 (z) f = 0, where k ≥ 2 is an integer and Bk-1 (z), ...,B1 (z),B0 (z) are analytic on an annulus. Under some conditions on the coefficients, we obtain some results concerning the estimates of the order and the hyper-order of solutions of the above equation. The results obtained extend and improve those of Wu and Xuan in [16]. [ABSTRACT FROM AUTHOR]

Green synthesis and metal oxide composites have attracted much attention from researchers of industry and academia. As a typical application of green synthesis and metal oxide composites, the continuous change of industrial technology and the continuous improvement of the social and economic level, the demand for oil and gas are also increasing. However, the spatial gap between the place of origin and the place of demand for oil and gas resources is large, so the long-distance oil and gas pipeline came into being. However, under the action of time, coupled with the corrosion effect of the soil due to deep burial, some pipelines have serious aging and corrosion phenomena. Therefore, in order to give corresponding guarantees for economic development, we need to conduct in-depth research and analysis of the corrosion of oil and gas long-distance pipelines and give effective solutions. In this paper, the corrosion rate prediction of buried oil and gas pipelines is studied in Changqing gas field. By improving the inertial weights and learning factors of the traditional particle swarm algorithm, the parameters of the generalized regression neural network are optimized and selected, and the corrosion rate prediction model of buried pipelines is finally constructed. Comparative analysis with other swarm intelligence algorithms shows that the improved particle swarm algorithm has stronger convergence ability and higher prediction accuracy than the BP model and SVM model. In addition, based on the detection data collected at the site of the gathering and transportation pipeline in Changqing gas field, this paper uses the extreme value distribution theory and the local corrosion progress formula to establish a prediction model for the residual life of corrosion of buried pipelines. The model established in this paper can effectively determine the risk pipe segment of buried pipeline and provide a decision-making basis for pipeline management departments. The work provides an important application guidance to green synthesis and metal oxide composites. [ABSTRACT FROM AUTHOR]

Using the traveling wave transformation, the seventh-order KdV equation reduces to a sixth-order complex differential equation (CDE), and we first prove that all meromorphic solutions of the CDE belong to the class W via Nevanlinna's value distribution theory. Then abundant new meromorphic solutions of the sixth-order CDE have been established in the finite complex plane with the aid of an extended complex method and Painlevé analysis, which contains Weierstrass elliptic function solutions and exponential function solutions, some of them are whole new solutions comparing to the opening literature. We give the computer simulations of some elliptic and exponential solutions. At last, we investigate the meromorphic solutions of the nonlinear dispersive Kawahara equation as an application. [ABSTRACT FROM AUTHOR]

Let X be a projective variety and D be an effective Cartier divisor on X. In Int J Math 32(12), Paper No. 2140015, 2021, He and Ru author introduced the notion of the Nevanlinna hyperbolicity for the pair (X, D). In this paper, we derive some further properties for the Nevanlinna hyperbolic pairs, as well as provide multiple examples of the Nevanlinna hyperbolic pairs (X, D), mainly for certain blowup varieties. [ABSTRACT FROM AUTHOR]

• A LASSO penalized approach for conducting variable selection for the extended partially linear single-index models • The local linear estimator for the nonparametric link function is shown to be oracally efficient • An asymptotically accurate simultaneous confidence band is derived for the nonparametric link function • Finite sample studies with commonly encountered sample sizes support the theoretical findings • Two engineering data analyses to illustrate the usefulness of the proposed method Substantial efforts have been made for the popular semiparametric single-index models in the last two decades. Extended partially linear single-index models as generalized single-index semiparametric models effectively reduce the problem of model misspecification by allowing the data to automatically choose the principal linear component and the principal nonlinear component. In this paper, we construct an oracle-efficient simultaneous confidence band as a global inference tool for the extended partially linear single-index models. Specifically, we apply a LASSO penalized local linear smoothing method to estimate the coefficient parameters and conduct variable selection to avoid model overfitting caused by the two appearances of covariates. It is shown that the local linear estimator for the nonparametric link function by employing the penalized coefficient estimates is oracle-efficient in the sense that it is uniformly as efficient as the ideal one obtained by utilizing the true coefficient parameters. Then by applying the oracle efficiency and the extreme value distribution theory of the local linear regression, an asymptotically accurate simultaneous confidence band for the nonparametric link function in the extended partially linear single-index models is established. Simulation experiments with commonly encountered sample sizes corroborate our theoretical findings. The proposed method is applied to analyze two engineering datasets: motor trend car road tests dataset and concrete slump tests dataset. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation fn(z) + Pd(z, f) = p1(z)eα1(z) + p2(z)eα2(z), where Pd(z, f) is a difference-differential polynomial in f(z) of degree d 6 n-1 with small functions of f(z) as its coefficients, p1, p2 are nonzero rational functions and α1, α2 are nonconstant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation. [ABSTRACT FROM AUTHOR]

In order to solve the problem that the F1-measure value and the AUROC value of some classical open-set classifier methods do not exceed 40% in high-openness scenarios, this paper proposes an algorithm combining negative-class feature enhancement learning and a Weibull distribution based on an extreme value theory representation method, which can effectively reduce the risk of open space in open-set scenarios. Firstly, the solution uses the negative-class sample feature enhancement learning algorithm to generate the negative sample point set of similar features and then compute the corresponding negative-class sample feature segmentation hypersphere. Secondly, the paired Weibull distributions from positive and negative samples are established based on the corresponding negative-class sample feature segmentation hypersphere of each class. Finally, solutions for non-linear multi-class classifications are constructed by using the Weibull and reverse Weibull distributions. Experiments on classic open datasets such as the open dataset of letter recognition, the Caltech256 open dataset, and the CIFAR100 open dataset show that when the openness is greater than 60%, the performance of the proposed method is significantly higher than other open-set support vector classifier algorithms, and the average is more than 7% higher. [ABSTRACT FROM AUTHOR]

Robinson, William I Can Global Capitalism Endure? This concise, lucid, and not very technical work illustrates how far global capitalism has gone under capital accumulation, value and financial appropriation, and digitalization. [Extracted from the article]

Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty)$ to general supports $(a, \infty)$ , $a > 0$. As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering. [ABSTRACT FROM AUTHOR]

In the paper, we formulate some open problems related to the best description of the values of the exceptional sets in Wiman's inequality for entire functions and in the Erdos-Macintyre type theorems for entire multiple Dirichlet series. At the same time, we clarify the statement of one I.V. Ostrovskii problem on Wiman's inequality. We also prove three propositions and one theorem. On the one hand, in a rather special case, these results give the best possible description of the values of the exceptional set in the Erdos-Macintyre-type theorem. On the second hand, they indicate the possible structure of the best possible description in the general case. [ABSTRACT FROM AUTHOR]

In this article, we obtain the Grunsky inequality and its several consequences for meromorphic univalent functions defined on the unit disk with a nonzero pole p ∈ (0,1) .As byproducts, we obtain the Goluzin and the Lebedev inequalities for these functions. We also obtain the Grunsky inequality for a subclass of aforesaid functions that have k-quasiconformal extensions onto the extended complex plane. [ABSTRACT FROM AUTHOR]

We consider the inverse resonance problem in scattering theory. In one-dimensional setting, the scattering matrix consists of 2 × 2 entries of meromorphic functions. The resonances are defined as the poles of the meromorphic determinant. For the compactly supported perturbation, we are able to quantitatively estimate the zeros and poles of each meromorphic entry. The size of potential support is connected to the zero density of scattered wave field due to the form of Fourier transform. We will investigate certain properties of Fourier transforms in scattering theory and derive the inverse uniqueness on scattering source given certain knowledge on the perturbation and all the given resonances. [ABSTRACT FROM AUTHOR]

The question at issue in this article is whether Richard Cantillon, notwithstanding his high reputation as an analyst of economic phenomena, failed to construct a tenable theory of value. That is a not uncommon allegation or implication found in the current literature. Several assessments of Cantillon's work do him a disservice by saddling him with a crude and unsatisfactory theory of value—specifically a "land-embodied" explanation of relative commodity values. That may at present be described as the dominant reading. While it is true that not all interpreters of Cantillon take the land-embodied line, it is nevertheless high time that the misrepresentation of Cantillon as the proponent of a land theory of value be called into question. This serious error needs to be highlighted and a proper understanding of Richard Cantillon's remarkably insightful analysis of distribution and value brought more firmly into mainstream thinking. This article wishes to establish that Cantillon was offering not—as alleged—a crude land-embodied explanation of relative values but, on the contrary, a viable cost-of-production treatment, set firmly in the contemporary social context (an approach that would be further developed by Smith and Marx as appropriate to later economic and social conditions). [ABSTRACT FROM AUTHOR]

V. Gupta introduced recently the Rathore type operators Rn,c. For them we obtain Voronovskaja type results. We extend the classical Szász-Mirakjan operator and compare the extension with Rn,c. [ABSTRACT FROM AUTHOR]

The composition Fn of Rathore and Gamma operators was considered in the literature. We introduce a generalization of Fn. For it we determine the eigenstructure and establish the corresponding Voronovskaja type formula. [ABSTRACT FROM AUTHOR]

We introduce homogeneous differential polynomials of a L-function and of a meromorphic function and investigate the uniqueness results using the concept of weakly weighted sharing. [ABSTRACT FROM AUTHOR]

In this paper, we establish analogous of Milloux inequality and Hayman's alternative for meromorphic functions in an angular domain. As an application of our results, we deduce some interesting analogous results for meromorphic function in an angular domain. And also we have given the applications of homogeneous differential polynomials to the Nevanlinna's theory of meromorphic functions in an angular domain and given some generalisations by these polynomials. [ABSTRACT FROM AUTHOR]

The continuous probability distributions have wide applications in the field of transportation and reliability engineering. The continuous distributions are used to estimate how funds can be allocated to improve roads, railways, bridges, waterways, airports etc. and used to check the reliability/performance of a product. The Gompertz exponential (GoE) distribution is derived using Gompertz G generator. Some basic properties of the model have been derived. The parameters of the GoE distribution are estimated by maximum likelihood estimation method. The upper record values from the GoE distribution have also been introduced with various properties. Moreover, applications of the GoE distributions has been provided in the field of reliability to check the performance of some transportation related parts and the suggested model provides better fit than the existing well-known models. Finally, a simulation study is carried out. Random numbers of size 50 are generated 15 times for GoE distribution and upper records has been noted. [ABSTRACT FROM AUTHOR]

In the paper, we study the value distribution of the differential polynomial ϕfn f(k) −1, where f(z) is a transcendental meromorphic function, ϕ(z)(̸≡ 0) is a small function of f(z) and n(> 2), k(≥ 1) are integers. We prove an inequality which will give an upper bound for the characteristic function T(r, f) in terms of reduced counting function only. [ABSTRACT FROM AUTHOR]

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results. [ABSTRACT FROM AUTHOR]

We study to determine the scattering source given certain knowledge of potential scatterer. In one-dimensional problem, the scattering matrix consists of 2 × 2 entries of meromorphic functions. Comparing other methods in problems of compactly supported perturbation, we are able to precisely and quantitatively estimate the zeros and poles of each meromorphic entry. The size of potential support is connected to the zero density of scattered wave field. Assuming that the known part of potential is supported more significantly than the unknown part, the latter is uniquely determined from the magnitude of transmission coefficient which is the magnitude of certain Fourier transform of traveling wave. We show that recovering of the unknown perturbation is possible through single direction measurements under certain assumptions. [ABSTRACT FROM AUTHOR]

Beijing-Tianjin-Hebei (BTH) is undergoing huge risks from severe precipitation extremes, but their climate features and underlying mechanisms are not fully understood and warrant in-depth investigations. Here, the summer extreme precipitation events in BTH are objectively divided into two types according to the spatial distribution i.e., Northeast precipitation (NEP) and Southwest precipitation (SWP) and their underlying mechanisms are revealed and compared from perspectives of circulation patterns and moisture transports. In the case of Type NEP , the anomalous deep low-pressure (high-pressure) systems respectively cover over the west (east) of BTH, which jointly induce strong anomalous southwesterly and southerly airflows converging over BTH. The converging airflows strengthen water vapor transports from the western and southern boundaries of BTH and result in a strong convection over northeastern BTH, thereby triggering Type NEP precipitation. Compared with Type NEP , the circulation pattern of Type SWP is characterized by an anomalous deep (shallow) high-pressure (low-pressure) system over northeast (southwest) of BTH, respectively. The circulation patterns could induce strong anomalous southerly and easterly airflows converging over BTH and thus strengthen water vapor transports from the southern and eastern boundaries of BTH, resulting in a strong convection over southwestern BTH. Over the long-term period, the summer extreme precipitation days with multiple return periods extracted by the Generalized extreme value distribution theory show significantly increasing trends in Beijing-Tianjin and surrounding areas, particularly in urban regions, indicating that summer extreme precipitation events are becoming more frequent. These findings provide theoretical basis for summer extreme precipitation forecasting and scientific insight for taking effective measures to mitigate the corresponding disasters in BTH. [Display omitted] • Two types' extreme precipitation events i.e., Northeast precipitation (NEP) and Southwest precipitation (SWP) are identified. • Diverse circulation patterns and moisture transports play key roles in determining rainfall centers of the two types events. • The sufficient moisture of Type NEP is mainly transported from the western and southern boundaries of BTH. • The sufficient moisture of Type SWP is mainly transported from the eastern and southern boundaries of BTH. • Summer extreme precipitation days with multiple return periods exhibit significantly increasing trends. [ABSTRACT FROM AUTHOR]

In this paper, we first obtain the famous Xiong Inequality for meromorphic functions in an angular domain and also generalise Nevanlinna's five-value theorem for derivatives of meromorphic functions by considering weaker assumptions of sharing five values and small functions to partially sharing k(≥ 5) values and small functions in an angular domain. As a particular cases of our results, we deduce He Ping result in an angular domain. [ABSTRACT FROM AUTHOR]

In this paper, we discuss how meromorphic functions are determined by their multiple values and deficient values in an angular domain and also we prove an at most 3-valued theorem for meromorphic function in an angular domain. [ABSTRACT FROM AUTHOR]

In this paper, we prove one value distribution result which leads to some normality criteria for a family of analytic functions. [ABSTRACT FROM AUTHOR]

In the paper, we study and compare relative (k, n) Valiron defect with the relative Nevanlinna defect for meromorphic function where k and n are both non negative integers on annuli. The results we proved are as follows 1. Let f(z) be a transcendental or admissible meromorphic function of finite order in A(R0), where 1 < R0 ≤ +∞ and Σ a≠∞ δ0(a, f) + δ0(∞, f) = 2. Then... 2. Let f(z) be a transcendental or admissible meromorphic function of finite order in A(R0), where 1 < R0 ≤ +∞ such that m0(r, f) = S(r, f). If a, b and c are three distinct complex numbers, then for any two positive integer k and n 3Rδ(0) 0(n)(a, f) + 2Rδ(0) 0(n)(b, f) + 3Rδ(0)0(n)(c, f) + 5RΔ(k) 0(n)(∞, f) ≤ 5RΔ(0) 0(n)(∞, f) + 5RΔ(k) 0(n)(0, f). 3. Let f(z) be a transcendental or admissible meromorphic function of finite order in A(R0), where 1 < R0 ≤ +∞ such that m0(r, f) = S(r, f). If a, b and c are three distinct complex numbers, then for any two positive integer k and n Rδ(0) 0(n)(0, f) +R Δ(k) 0(n)(∞, f) +Rδ(0)0(n)(c, f) ≤R Δ(0) 0(n)(∞, f) + 2RΔ(k) 0(n)(0, f). 4. Let f(z) be a transcendental or admissible meromorphic function of finite order in A(R0), where 1 < R0 ≤ +∞ such that m0(r, f) = S(r, f). If a and d are two distinct complex numbers, then for any two positive integer k and p with 0 ≤ k ≤ p Rδ(0) 0(n)(d, f) +R Δ(p) 0(n)(∞, f) +R δ(k) 0(n)(a, f) ≤R Δ(k) 0(n)(∞, f) +R Δ(p) 0(n)(0, f) +R Δ(k)0(n)(0, f), where n is any positive integer. 5.Let f(z) be a transcendental or admissible meromorphic function of finite order in A(R0), where 1 < R0 ≤ +∞. Then for any two positive integers k and n, RΔ(0) 0(n)(∞, f) +R Δ(k) 0(n)(0, f) ≥R δ(0) 0(n)(0, f) +R δ(0) 0(n)(a, f) +R Δ(k) 0(n)(∞, f), where a is any non zero complex number. [ABSTRACT FROM AUTHOR]

This article introduces a new evolving fuzzy-rule-based algorithm for online data streams, named extreme value evolving predictor (EVeP). It offers a statistically well-founded approach to define the evolving fuzzy granules that form the antecedent and the consequent parts of the rules. The evolving fuzzy granules correspond to radial inclusion Weibull functions. They are interpreted by the extreme value theory as the limiting distribution of the relative proximity among the rules of the learning model. Regarding the parameters of the Takagi–Sugeno term at the consequent of the rules, the algorithm enhances the already demonstrated benefits of multitask learning by replacing a binary version with a fuzzy structural relationship among the rules. The pairwise similarity among the rules is automatically provided by the current interaction of the evolving fuzzy granules at the antecedent and at the consequent parts of their corresponding rules. Several computational experiments, using artificial and real-world time series, attest to the dominating prediction performance of EVeP when compared to the state-of-the-art evolving algorithms. [ABSTRACT FROM AUTHOR]

For derived curves intersecting a family of decomposable hyperplanes in subgeneral position, we obtain an analog of the Cartan–Nochka Second Main Theorem, generalizing a classical result of Fujimoto about decomposable hyperplanes in general position. [ABSTRACT FROM AUTHOR]

Motivated by the notion of the algebraic hyperbolicity, we introduce the notion of Nevanlinna hyperbolicity for a pair (X , D) , where X is a projective variety and D is an effective Cartier divisor on X. This notion links and unifies the Nevanlinna theory, the complex hyperbolicity (Brody and Kobayashi hyperbolicity), the big Picard-type extension theorem (more generally the Borel hyperbolicity). It also implies the algebraic hyperbolicity. The key is to use the Nevanlinna theory on parabolic Riemann surfaces recently developed by P ă un and Sibony [Value distribution theory for parabolic Riemann surfaces, preprint (2014), arXiv:1403.6596]. [ABSTRACT FROM AUTHOR]

In this paper, it is the multivariate Nevanlinna value distribution theory and difference simulation results, the properties of solutions to two types of generalized Fermat-type partial differential-difference equations are discussed. The existence condition of the solution of the finite-order transcendental integral function of the equation containing one, two partial differentials and differences and the form of the solution are obtained, and an example is given to illustrate the solution the accuracy oft the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we studied the well posedness for a new class of optimization problems with variational inequality constraints involving second-order partial derivatives. More precisely, by using the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity for a multiple integral functional, and by introducing the set of approximating solutions for the considered class of constrained optimization problems, we established some characterization results on well posedness. Furthermore, to illustrate the theoretical developments included in this paper, we present some examples. [ABSTRACT FROM AUTHOR]

We study the value distribution theory of L-functions and completely resolve a question from Yang [10]. This question is related to L-functions sharing three finite values with meromorphic functions. The main result in this paper extends corresponding results from Li [10]. [ABSTRACT FROM AUTHOR]

This paper relates to a recent trend in complex differential equations which studies solutions in a given domain. The classical settings in complex equations were widely studied for meromorphic solutions in the complex plane. For functions in the complex plane, we have a lot of results of general nature, in particular, the classical value distributions theory describing numbers of a-points. Many of these results do not work for functions in a given domain. A recent principle of derivatives permits us to study the numbers of Ahlfors simple islands for functions in a given domain; the islands play, to some extend, a role similar to that of the numbers of simple a-points. In this paper, we consider a large class of higher order differential equations admitting meromorphic solutions in a given domain. Applying the principle of derivatives, we get the upper bounds for the numbers of Ahlfors simple islands of similar solutions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the uniqueness of meromorphic functions sharing a set with counting multiplicity and also with weight 1 in an angular domain. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the algebroid functions W(z) and W′(z) that share the value 1 CM (counting multiplicities) and share one finite value DM (different multiplicities) with derivative on annuli. [ABSTRACT FROM AUTHOR]

With the exception of Pasinetti's work on structural change, the sraffian literature remains silent on normative issues. By generalizing Smith's notion of free competition, this paper identifies and formalizes an ideal social arrangement yielding a unique income distribution configuration which is fair in terms of the "equality of opportunity" norm, and which can be used as a benchmark for normative analysis in Sraffa's system. In this hypothetical economy, the price vector, the wage rate and the profit rates depend only on physical quantities. The relation between this result and Sraffa's "physical real cost" theory of value and distribution is also discussed. [ABSTRACT FROM AUTHOR]

In this paper we deal with the uniqueness problem of the power of a meromorphic function when it shares a set with its derivative. We also relax the nature of sharing of the set and reduce the cardinality of the shared set in some cases. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the uniqueness problem of meromorphic functions ordinarily and partially sharing values with the reduced linear c-shift operators governed by them, which practically provide an extensions and improvements of a number of recent results at a large extent. [ABSTRACT FROM AUTHOR]

In this paper, by making use of q-derivative we introduce a new subclass of meromorphically univalent functions. Precisely, we give a necessary and sufficient coefficient condition for functions in this class. Coefficient estimates, extreme points, convex linear combination Radii of starlikeness and convexity and finally partial sum property are investigated. [ABSTRACT FROM AUTHOR]