Qualitative properties of Hénon type equations with exponential nonlinearity

We are interested in the qualitative properties of solutions of the Hénon type equations with exponential nonlinearity. First, we classify the stable at infinity solutions of Δu + |x| α e u = 0 in R N , which gives a complete answer to the problem considered in Wang and Ye (2012 J. Funct. Anal. 262 1705–1727). Secondly, existence and precise asymptotic behaviours of entire radial solutions to Δ2 u = |x| α e u are obtained. Then we classify the stable and stable at infinity radial solutions to Δ2 u = |x| α e u in any dimension.

THE HYPOTHESIS OF THE ARSACIDS’ DESCENT FROM THE ACHAEMENIDS: MYTH OR REALITY?

In the 40s of the last century, J. Wolski proposed a thesis, still dominant in historiography, arguing that the story of Arrian which reached us thanks to his work “Parthica” that the Arsacid dynasty, the founder of Parthian state, descended from the Achaemenids, has a fictional origin. According to J. Wolski, J. Neusner and their followers, it is an "ideological fiction", a "literary forgery", which appeared in the period between the second half of II century BC and the beginning of the I century AD and was recorded in written form by Arrian. However, the conclusion, based on the limited and often one-sided data by Strabo and Justin, is defective and does not meet the current requirements of the study of the problem. Оnly a comprehensive examination of the evidence provided by written sources in the field of the Parthian numismatics, epigraphy, archaeology, onomastics and other branches of science can give a complete answer to the issue. In this case, it becomes obvious that the "Arrianian" legend about the genealogical connection between the Arsacids and the Achaemenids is not just a literary fiction, but has a real historical basis.

The Aim of Inquiry

I defend the thesis that the constitutive aim of inquiring into some question, Q, is improving one’s epistemic standing with respect to Q. Call this the epistemic-improvement view. I consider and ultimately reject two alternative accounts of the constitutive aim of inquiry—namely, the thesis that inquiry aims at knowledge and the thesis that inquiry aims at (justified) belief—and I use my criticisms as a foil for clarifying and motivating the epistemic-improvement view. I also consider and reject a pair of normative theses about when inquiry goes awry or is inappropriate. The first is the normative thesis defended by Dennis Whitcomb who claims that inquiry goes awry if it culminates in a belief that falls short of knowledge and that one should not inquire into Q if one already knows the answer to Q. The second is the normative thesis defended by Jane Friedman who claims that one should not inquire into Q if one already believes some complete answer to Q.

Union at the Centre

The devolution settlement of 1999 introduced radical changes at the periphery but changed almost nothing at the centre. England remained subject directly to the Westminster Parliament and UK Government, so the system is asymmetrical. Intergovernmental relations are weakly institutionalized. While UK Governments have not systematically intervened in devolved matters, Whitehall departments are often insensitive to the effects of their decisions on Scotland, Wales and Northern Ireland. England is not represented in the constitutional settlement but an English level of politics and administration has emerged by subtraction of the devolved territories. An inchoate sense of dissatisfaction has crystalized around the issues of ‘English votes for English laws’ and the supposedly favourable treatment for Scotland I public expenditure. As long as the English Question is poorly specified, a more complete answer to it remains elusive.

From maximality to bias: Biased A-not-A questions in Mandarin Chinese

This study aims to derive the epistemic bias in shi-bu-shi questions, a type of A-not-A question in Mandarin Chinese. I propose: (i) the focus marker shi presupposes that its prejacent is a possible complete answer to the current Question Under Discussion (QUD); (ii) accordingly, shi-bu-shi questions are presupposed to be part of the Focus-strategy of inquiry; (iii) the Focus-strategy of inquiry indicates the questioner's intention to close the current QUD as soon as possible, and to achieve this goal, the questioner should check the answer that she considers most likely to be true. By assuming such completeness-to-likelihood reasoning, a novel link between focus in polar questions and question bias is established. The ramifications of this proposal for related phenomena (e.g., bias in embedded questions, evidential bias) are then discussed.

Toughness, Forbidden Subgraphs and Pancyclicity

Motivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$ K 1 ∪ P 4 can act as a forbidden subgraph to ensure that every 1-tough H-free graph is hamiltonian, and that there is no other forbidden subgraph with this property, except possibly for the graph $$K_1\cup P_4$$ K 1 ∪ P 4 itself. The hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs, as conjectured by Nikoghosyan, was left there as an open case. In this paper, we consider the stronger property of pancyclicity under the same condition. We find that the results are completely analogous to the hamiltonian case: every graph H such that any 1-tough H-free graph is hamiltonian also ensures that every 1-tough H-free graph is pancyclic, except for a few specific classes of graphs. Moreover, there is no other forbidden subgraph having this property. With respect to the open case for hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs we give infinite families of graphs that are not pancyclic.

Una nueva solución al problema de la fundamentación

Let us consider a statue and the piece of clay out of which it is made, and let us suppose that they start to exist and cease to exist at exactly the same time. According to colocationism, the statue and the piece of clay are two different objects: they have different properties (for example, one is a statue and the other a piece of clay) and, according to Leibniz’s Law, the same object cannot have different properties. One of the most difficult questions for colocationism is that of the grounding problem: given that the statue and the piece of clay share many of their properties (their matter, their microscopic composition, their structure, etc.), what is it that grounds the fact that they have different sortal (or modal) properties? Recently, Catherine Sutton has offered a very interesting answer to the question. However, as I will argue, it cannot be applied to all cases of colocated objects and therefore, it is not an adequate solution to the grounding problem. The main objective of this paper is to present a new solution to the grounding problem that integrates some of Sutton’s theses, but that allows us to give a complete answer to the question. To do this, the notion of a process of coming into existence will be crucial. After presenting the new proposal, I will compare it with the proposals by Kit Fine and Noël Saenz.

Concentration of Product Spaces

We investigate the relation between the concentration and the product of metric measure spaces. We have the natural question whether, for two concentrating sequences of metric measure spaces, the sequence of their product spaces also concentrates. A partial answer is mentioned in Gromov’s book [4]. We obtain a complete answer for this question.

Factorization and Malleability of RSA Moduli, and Counting Points on Elliptic Curves Modulo N

In this paper we address two different problems related with the factorization of an RSA (Rivest–Shamir–Adleman cryptosystem) modulus N. First we show that factoring is equivalent, in deterministic polynomial time, to counting points on a pair of twisted Elliptic curves modulo N. The second problem is related with malleability. This notion was introduced in 2006 by Pailler and Villar, and deals with the question of whether or not the factorization of a given number N becomes substantially easier when knowing the factorization of another one N′ relatively prime to N. Despite the efforts done up to now, a complete answer to this question was unknown. Here we settle the problem affirmatively. To construct a particular N′ that helps the factorization of N, we use the number of points of a single elliptic curve modulo N. Coppersmith’s algorithm allows us to go from the factors of N′ to the factors of N in polynomial time.

The Effect of Points Fattening on del Pezzo Surfaces

In this paper, we study the fattening effect of points over the complex numbers for del Pezzo surfaces $$\mathbb {S}_r$$ S r arising by blowing-up of $$\mathbb {P}^2$$ P 2 at r general points, with $$ r \in \{1, \dots , 8 \}$$ r ∈ { 1 , ⋯ , 8 } . Basic questions when studying the problem of points fattening on an arbitrary variety are what is the minimal growth of the initial sequence and how are the sets on which this minimal growth happens characterized geometrically. We provide a complete answer for del Pezzo surfaces.