Functionally Separation Axioms on General Topology

In this paper, we define a new family of separation axioms in the classical topology called functionally T i spaces for i = 0,1,2 . With the assistant of illustrative examples, we reveal the relationships between them as well as their relationship with T i spaces for i = 0,1,2 . We demonstrate that functionally T i spaces are preserved under product spaces, and they are topological and hereditary properties. Moreover, we show that the class of each one of them represents a transitive relation and obtain some interesting results under some conditions such as discrete and Sierpinski spaces.

Types of Complex Fuzzy Relations with Applications in Future Commission Market

In this paper, we introduce types of relations on complex fuzzy sets such as the complex fuzzy (CF) inverse relation, complex fuzzy reflexive relation, complex fuzzy symmetric relation, complex fuzzy antisymmetric relation, complex fuzzy transitive relation, complex fuzzy irreflexive relation, complex fuzzy asymmetric relation, complex fuzzy equivalence relation, and complex fuzzy-order relation. We study some basic results and particular examples of these relations. Moreover, we discuss the applications of complex fuzzy relations in Future Commission Market (FCM). We show that the introduction of CF relations to applications of FCMs can give a significant method for describing the temporal dependence between parameters of a Future Commission Market.

Groups satisfying the minimal condition on subgroups which are not transitively normal

A subgroup X of a group G is called transitively normal if X is normal in any subgroup Y of G such that $$X\le Y$$ X ≤ Y and X is subnormal in Y. Thus all subgroups of a group G are transitively normal if and only if normality is a transitive relation in every subgroup of G (i.e. G is a $$\overline{T}$$ T ¯ -group). It is proved that a group G with no infinite simple sections satisfies the minimal condition on subgroups that are not transitively normal if and only if either G is Černikov or a $${\overline{T}}$$ T ¯ -group.

On non-normal cyclic subgroups of prime order or order 4 of finite groups

In this paper, we call a finite group G G an N L M NLM -group ( N C M NCM -group, respectively) if every non-normal cyclic subgroup of prime order or order 4 (prime power order, respectively) in G G is contained in a non-normal maximal subgroup of G G . Using the property of N L M NLM -groups and N C M NCM -groups, we give a new necessary and sufficient condition for G G to be a solvable T T -group (normality is a transitive relation), some sufficient conditions for G G to be supersolvable, and the classification of those groups whose all proper subgroups are N L M NLM -groups.

A Variety of Causes

Metaphysicians often focus on what is vertically fundamental, appealing to grounding or truth-making, rather than what is horizontally fundamental: what must be common to any metaphysical picture of the universe. There is a case for causation being one such feature. But how should it be characterized? A revised semantics for counterfactuals provides the basis for a new counterfactual analysis of causation that is compatible with Humean supervenience but also appropriate for a non-Humean metaphysical framework. Causes (independently of their competitors) both make the chance of an effect very much greater than its mean background chance in the circumstances and actually influences the probability of the effect in this way at the time at which the effect occurred via a complete causal chain. Causation understood in this way is a non-transitive relation. It is neutral over the metaphysics of causes and effects but allows a natural way for events to be understood as one fundamental type of causation, the other being property causation. Although negative causal statements are true, there are no cases of negative causation. The analysis explains how causation involving substantial processes is only one variety of causation, others include double prevention. It allows for a variety of micro- and macro-properties to be the basis of the difference between cause and effect. Laws are patterns of causation realized in different ways in different metaphysical pictures. The analysis of causation characterizes a horizontally fundamental property whose modal character depends upon its different realizations.

A linguistic study on rhyming in the Beijing dialect/ 北京歌谣押韵的语言学研究

Rhyming plays an important role in the study of Chinese phonology. Traditionally it is believed that there are two types of rhyming between finals: free rhyming and mixed rhyming. Finals which rhyme with each other freely constitute a rhyme group, while the rhyming between finals from different rhyme groups can only be mixed rhyming. By analyzing the rhyming in the modern Beijing dialect using a statistical method, we find a third type: semi-free rhyming, which is close to free rhyming. As a whole, these two types can be called pan-free rhyming. Thus, the definition of rhyme group must be revised as the maximum unit of pan-free rhyming, because free rhyming is no longer a transitive relation, i.e., when both final pairs A–B and B–C are free rhyming, A–C may be semi-free rhyming. As for the Beijing dialect, our statistical test results approve that non-érhuà finals are divided into 15 rhyme groups, and subsequent phonological analyses show that words in the same rhyme group share the same nucleus and coda. Besides finals, tones also function apparently in rhyming, but in a different way from the three types mentioned above. As more Chinese dialects are studied, the typology of rhyming in Chinese dialects can be analyzed, creating a useful reference for the study of Chinese historical phonology.

Coreference De Jure

In the recent literature, the relation of coreference de jure (the CDJ relation, for short) is characterized roughly as follows: that relation holds between two singular terms (tokens) in a discourse just in case whoever understands the discourse knows that the two terms corefer if they refer at all. In the mental file framework, adopted here, this is cashed out by saying that the two terms are associated with the same mental file. This chapter discusses various alleged properties of the CDJ relation: factivity, transparency, and transitivity. It is argued that (i) the CDJ relation can be both factive and transparent, while (ii) we need to distinguish between two sorts of coreference de jure, only one of which is a transitive relation.

Bipolar Fuzzy Relations

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

On the satisfiability problem for fragments of two-variable logic with one transitive relation

We study the satisfiability problem for two-variable first-order logic over structures with one transitive relation. We show that the problem is decidable in 2-NExpTime for the fragment consisting of formulas where existential quantifiers are guarded by transitive atoms. As this fragment enjoys neither the finite model property nor the tree model property, to show decidability we introduce a novel model construction technique based on the infinite Ramsey theorem. We also point out why the technique is not sufficient to obtain decidability for the full two-variable logic with one transitive relation; hence, contrary to our previous claim, [FO$^2$ with one transitive relation is decidable, STACS 2013: 317-328], the status of the latter problem remains open.