Temporal–Spatial Evolution and Influencing Factors of Coordinated Development of the Population, Resources, Economy and Environment (PREE) System: Evidence from 31 Provinces in China

Facing the increasingly severe friction among the domains of population, resources, economy and environment (PREE) in a system, theoretical guidance for the sustainable development of a PREE system can be obtained by exploring the coordinated development of a PREE system during its temporal–spatial evolution process. Based on the PREE data of 31 provinces in China from 2010 to 2019, this study uses a spatial measurement method to analyze the temporal and spatial evolution characteristics of the PREE systems of China’s provinces. The results show that the overall coordination level of China’s provincial PREE systems fluctuated but improved from moderate imbalance to moderate coordination. However, the differences in the regional coordination level first decreased and then increased. The distribution characteristics of the system coordination level changed from “high in the east and low in the west” to “high in the west and low in the east”, resulting in the “inversion” phenomenon of the system coordination level. The spatial correlation of the coordination level of the PREE system among provinces and cities gradually increased. The coordination level of the PREE system in the eastern, central and western regions was noticeably different, accompanied by different degrees of polarization and showing different dynamic evolution trends. In the analysis of influencing factors, it was found that seven factors, such as per capita GDP, the proportion of environmental pollution control investment to GDP and per capita energy production, promoted the coordinated development of China’s PREE system to varying degrees. The coordinated and stable development of China’s PREE system should be adjusted and optimized from the perspectives of different regions, scales and systems.

Singularly perturbed dynamics of the tippedisk

The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disc, being reminiscent of (but different from) the well-known inversion of the tippetop. A reduced model of the tippedisk, in the form of a three-dimensional ordinary differential equation, has been derived recently, followed by a preliminary local stability analysis of stationary spinning solutions. In the current paper, a global analysis of the reduced system is pursued using the framework of singular perturbation theory. It is shown how the presence of friction leads to slow–fast dynamics and the creation of a two-dimensional slow manifold. Furthermore, it is revealed that a bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation leads to an explanation of the inversion phenomenon. In particular, a closed-form condition for the critical spinning speed for the inversion phenomenon is derived. Hence, the tippedisk forms an excellent mathematical-mechanical problem for the analysis of global bifurcations in singularly perturbed dynamics.

Model reduction of the tippedisk: a path to the full analysis

The tippedisk is a mechanical-mathematical archetype for friction-induced instability phenomena that exhibits an interesting inversion phenomenon when spun rapidly. The inversion phenomenon of the tippedisk can be modeled by a rigid eccentric disk in permanent contact with a flat support, and the dynamics of the system can therefore be formulated as a set of ordinary differential equations. The qualitative behavior of the nonlinear system can be analyzed, leading to slow–fast dynamics. Since even a freely rotating rigid body with six degrees of freedom already leads to highly nonlinear system equations, a general analysis for the full system equations is not feasible. In a first step the full system equations are linearized around the inverted spinning solution with the aim to obtain a local stability analysis. However, it turns out that the linear dynamics of the full system cannot properly describe the qualitative behavior of the tippedisk. Therefore, we simplify the equations of motion of the tippedisk in such a way that the qualitative dynamics are preserved in order to obtain a reduced model that will serve as the basis for a following nonlinear stability analysis. The reduced equations are presented here in full detail and are compared numerically with the full model. Furthermore, using the reduced equations we give approximate closed form results for the critical spinning speed of the tippedisk.

The Structure of Interrogative Sentences with a Nominal Subject in the French Language in a Diachronic Aspect

The article is focused on the study of interrogative sentences with a nominal subject in the French language in terms of structural criteria in a diachronic aspect. The purpose of this study is to reveal the features of the so-called complex inversion in interrogative sentences. Special attention is paid to terminological problems. Pronominal reprise is recognized by the authors as the most correct term for an interrogative construction with a nominal subject duplicated by a personal pronoun. The lack of uniformity in terminology indicates a multidimensional nature of the inversion phenomenon in the French language. For instance, in addition to interrogative sentences, it can be used in other contexts: in simple declarative sentences after certain adverbs, in subordinate clauses after some conjunctions, in exclamatory sentences, etc. The authors highlight and describe the characteristic features of interrogative sentences with a nominal subject in terms of diachrony. Pronominal reprise appears in interrogative constructions as early as in the 16th century, mainly in general questions, subsequently extending to special questions. In the 16th – 17th centuries, the subject did not regularly precede the verb; the same applied to interrogative words, which could be placed both to the left and to the right of the subject. In sentences with a nominal subject, reprise was not the only possible structural option. The following were also used: direct word order, construction question word + est-ce que, and simple inversion. The authors come to the conclusion that pronominal reprise had finally replaced simple inversion of the nominal subject in general questions in French by the end of the 17th century.

The Power Of The Mysterious Inversion In Literary Books

Language is a great blessing given to humanity, literary devices that make the language shiny, colorful, meaningful, an inversion literary device that enhances clarity with formality and emphasis, its importance and important functions, types, uses and the Uzbek writer Tahir Malik skillfully used inversion in "Samum" and skillfully interpreted the words of the inversion phenomenon in the work and skillfully conveyed it to the reader, and words in literary books the features of magic enhancement, translation studies on inversion, and their importance are covered in detail in this article.

AZƏRBAYCAN VƏ İNGİLİS DİLLƏRİNDƏ İNVERSİYA HADİSƏSİ VƏ ONUN SADƏ CÜMLƏ TƏRKİBİNDƏ İFADƏSİ

Məqalə müxtəlifsistemli olan azərbaycan və ingilis dillərində söz sırasına və onun cümlədə ifadəsinə həsr olunmuşdur. Hər iki dildə nəqli cümlələr sabit söz sırasına malikdir. Hər bir cümlə üzvü müəyyən mövqelərdə yerləşir və söz sırasının pozulması mənanın dəyişməsinə və ya cümlədə mənanın itməsinə gətirib çıxarır. İngilis dilində cümlədə söz sırası mübtəda, xəbər, tamamlıq, zərflik ardıcıllığı üzrə formalaşır. İngilis dilində sual cümlələrinin inversiyası geniş yayılmışdır. Belə cümlələrin xüsusi intonasiyası və kommunikativ məqsədi olur. Məlum olur ki, sözlərin sıralanması və bu xüsusda meydana çıxan inversiya hadisəsi məsələsi həmişə dilçilərin diqqət mərkəzində olmuşdur. Söz sırası mətnin təşkilində həm qrammatik, həm də üslubi funksiya daşıyır. Başqa sözlə, söz sırası həm bilavasitə əlaqələrin yaranmasında, komponentlərin bir-biri ilə qrammatik əlaqəsinə kömək edir, həm də emosionallığa xidmət edir. Azərbaycan dilçiliyində S.Cəfərov, O.Musayev, R.Xəlilov, Ş.Yusifli, Ə.Cavadov, M.Bayramov; ingilis dilçiliyində M.Lazarkeviç, T.Koblens və başqaları bu problemlə bağlı araşdırmalar aparmışlar. Onlar belə nəticəyə gəlmişlər ki, hər bir dil hadisəsi kimi, cümlədə sözlərin sıralanması da müəyyən qanunlar əsasında baş verir. Bilirik ki, mətn cümlələr vasitəsilə reallaşır. Söhbət təkcə mətnin reallaşmasından getmir, əsas məsələ mətndəki mövzunun qavranılmasından gedir. Bununla yanaşı, mübahisəli məsələlər də mövcuddur. Bu da ondan ibarətdir ki, dildə vahid sıra sisteminin qanunauyğunluğu müəyyənləşmədiyi üçün hansı cümlənin birinci sıraya, hansı cümlənin isə çevrilmə olduğu dəqiq göstərilməmişdir, yəni araşdırma bir tərəfli aparılmışdır. Beləliklə, bir dil hadisəsi kimi sıralanmanın məzmun və mahiyyəti açılmamış, sintaktik vahidlərin sıralanmasından təcrid edilmiş şəkildə söhbət getmiş, fikrimizcə, sıra bir sistem, kateqoriya kimi nəzərdə tutulmamışdır. Inversion phenomenon in Azerbaijani and English languages and its expression in simple sentences- mövzumun ingilis dilində adı Açar sözlər: söz sırası, inversiya, mətn əlaqələri, sıralanma qanunları, presuppozisiya

Rethinking ‘residual’ Verb Second

The term “residual Verb Second ” is a misnomer for English, because V2 is, in fact, still productive in the language. Evidence for this comes from a previously undescribed negative inversion phenomenon innovated very recently in varieties of English. An analysis is proposed for how such a restrictive V2 system could, nevertheless, be productive, appealing to learner-driven models of language change in which novel structures can arise as artefacts of the acquisition procedure. Specifically, it is argued that innovative V2 arises when acquirers postulate a novel clause type characterized by a left-edge operator, which they analyse as a V2 environment by analogy with other non-declarative clause types involving such structures (e.g. interrogatives). This finds support from other cases of innovative V2 in English, Scots, and Afrikaans. Overall, we are left with a clearer picture of the status of V2 in English, and what it takes to innovate new V2 environments cross-linguistically.

Systematic Experimental Investigation of Segregation Direction and Layer Inversion in Binary Liquid-Fluidized Bed

Multi-component liquid-fluidized beds are encountered in a variety of industrial processes. Often, segregation severely affects the performance of the process unit. Unfortunately, size-driven and density-driven separation processes may occur with a complex interplay, showing prevailing mechanisms that change with the operating conditions. For example, when the solids exhibit contrasting differences in size and density, even the direction of segregation can turn out hard to predict, giving rise for some systems to the so-called “layer inversion phenomenon”. A systematic experimental investigation is presented on 14 different binary beds composed of glass beads and ABS spheres with different size and density ratios and different bed composition. The analysis allows assessing the reliability of a model for predicting the segregation direction of fluidized binary beds (the Particle Segregation Model, PSM). By measurements of the solids’ concentration at the surface, expansion/segregation properties and the inversion voidage are compared with the PSM predictions, offering a direct means of model validation. Both the segregation direction throughout the expansion range and the value of the inversion voidage are compared. Extensive qualitative agreement is obtained for 12 out of 14 fluidized mixtures. Quantitatively, the average discrepancy between predicted and measured inversion voidage is below 5%, with a maximum of 17%.