On minimal log discrepancies and kollár components

In this article, we prove a local implication of boundedness of Fano varieties. More precisely, we prove that $d$ -dimensional $a$ -log canonical singularities with standard coefficients, which admit an $\epsilon$ -plt blow-up, have minimal log discrepancies belonging to a finite set which only depends on $d,\,a$ and $\epsilon$ . This result gives a natural geometric stratification of the possible mld's in a fixed dimension by finite sets. As an application, we prove the ascending chain condition for minimal log discrepancies of exceptional singularities. We also introduce an invariant for klt singularities related to the total discrepancy of Kollár components.

Semigroups whose right ideals are finitely generated

We call a semigroup $S$ weakly right noetherian if every right ideal of $S$ is finitely generated; equivalently, $S$ satisfies the ascending chain condition on right ideals. We provide an equivalent formulation of the property of being weakly right noetherian in terms of principal right ideals, and we also characterize weakly right noetherian monoids in terms of their acts. We investigate the behaviour of the property of being weakly right noetherian under quotients, subsemigroups and various semigroup-theoretic constructions. In particular, we find necessary and sufficient conditions for the direct product of two semigroups to be weakly right noetherian. We characterize weakly right noetherian regular semigroups in terms of their idempotents. We also find necessary and sufficient conditions for a strong semilattice of completely simple semigroups to be weakly right noetherian. Finally, we prove that a commutative semigroup $S$ with finitely many archimedean components is weakly (right) noetherian if and only if $S/\mathcal {H}$ is finitely generated.

Measurable Riesz spaces

We study measurable elements of a Riesz space $E$, i.e. elements $e \in E \setminus \{0\}$ for which the Boolean algebra $\mathfrak{F}_e$ of fragments of $e$ is measurable. In particular, we prove that the set $E_{\rm meas}$ of all measurable elements of a Riesz space $E$ with the principal projection property together with zero is a $\sigma$-ideal of $E$. Another result asserts that, for a Riesz space $E$ with the principal projection property the following assertions are equivalent. (1) The Boolean algebra $\mathcal{U}$ of bands of $E$ is measurable. (2) $E_{\rm meas} = E$ and $E$ satisfies the countable chain condition. (3) $E$ can be embedded as an order dense subspace of $L_0(\mu)$ for some probability measure $\mu$.

Chain Condition and Fundamental Relation on (∆;G)-Sets Derived from Gamma-Semihypergroups

The aim of this research work is to define a new class of hyperstructure as a generalization of semigroups, semihypergroups and Γ-semihypergroups that we call (Δ,G)-sets. Also, we define fundamental relation on (Δ,G)-sets and prove some results in this respect. Then, we introduce the notions of quotient (Δ,G)-sets by using a congruence relations. Finally, we introduce the concept of complete parts and Noetherian(Artinian) (Δ,G)-sets.

Analysis of Supply Chain Management of Lobster (Panulirus spp.) In Pangandaran (Case Study of PT. ASI Pudjiastuti Marine Product)

This study aims to analyze supply chain management of lobster in Pangandaran especially PT. ASI Pudjiastuti Marine Product. The research method is a case study with the case unit at PT. ASI Pudjiastuti Marine Product while information would be collected through primary and secondary data in the field. The sampling method in this research used snowball sampling. The research was conducted from August 2020 - September at TPI Pangandaran and PT. ASI Pudjiastuti Marine Product. The criteria used to select respondents in this study as follow; 4 fishermen, 3 distributors, 2 employees of PT. ASI Pudjiastuti Marine Product and 1 retailer. And the data would be analyzed to get the supply chain condition of lobster. The results showed that there were 6 marketing channels in the supply chain of lobster in Pangadaran case study of PT. ASI Pudjiastuti Marine Product. The availability of lobster products has a value of 0.5 which means was not easily replaced and needed. Late payment and distribution of lobster have a value of 1.0 which means irreplaceable and important. The third and fourth chain marketing margins are below 50%, which means efficient for all members of the chain. The fifth chain has 46.55% and it’s inefficient Fisherman's share. The largest market share value was 46.40% on the fifth channel. Supply chain of lobster in Pangandaran has 6 marketing channels which third and fourth are the most efficient for all members, and the second is most profitable for PT ASI.

Banach algebras satisfying certain chain conditions on closed ideals

Let 𝔄 be a unital Banach algebra and ℜ its Jacobson radical. This paper investigates Banach algebras satisfying some chain conditions on closed ideals. In particular, it is shown that a Banach algebra 𝔄 satisfies the descending chain condition on closed left ideals then 𝔄/ℜ is finite dimensional. We also prove that a C*-algebra satisfies the ascending chain condition on left annihilators if and only if it is finite dimensional. Moreover, other auxiliary results are established.

On Modules Satisfying the Descending Chain Condition on Cyclic Submodules

A module satisfying the descending chain condition on cyclic submodules is called coperfect. The class of coperfect modules lies properly between the class of locally artinian modules and the class of semiartinian modules. Let R be a commutative ring with identity. We show that every semiartinian R-module is coperfect if and only if R is a T-ring. It is also shown that the class of coperfect R-modules coincides with the class of locally artinian R-modules if and only if 𝔪/𝔪2 is a finitely generated R-module for every maximal ideal 𝔪 of R.

Groups satisfying the double chain condition on non-subnormal subgroups

If 𝜃 is a subgroup property, a group 𝐺 is said to satisfy the double chain condition on 𝜃-subgroups if it admits no infinite double sequences\cdots<X_{-n}<\cdots<X_{-1}<X_{0}<X_{1}<\cdots<X_{n}<\cdotsconsisting of 𝜃-subgroups. The structure of generalised radical groups satisfying the double chain condition on non-subnormal subgroups is described.

Comparative Study of Extreme Value Estimation Approaches for Mooring Lines Top Tension Responses

It is known that the mooring system response of floating production units subjected to environmental loads is nonlinear. Even though wave elevations can be assumed as Gaussian processes for short-term periods, corresponding line tension responses generally are not, due to second-order slow-drift floater motions and intrinsic nonlinearities of the system. In this work, short-term extreme responses are estimated based on two different approaches. In the first one, a number of probability distributions are fitted to the tension time histories’ peaks samples and classic order statistics is applied to determine the most probable extreme line tension corresponding to a short-time period (3-h) in order to identify the one with best performance. The effect of correlation between consecutive peaks in the extremes estimation is investigated through the one-step Markov chain condition by using a Nataf transformation-based model. In the second approach, a more robust and recently developed method named average conditional exceedance rate (ACER) is investigated, where dependencies between maxima can be easily taken into account. Additionally, effects of major parameters in dynamic analyses, such as simulation length and discretization level of the wave spectrum, are evaluated. All time-series-based extreme estimates are compared with the estimates directly obtained from a sample of epochal maxima (Gumbel method). Numerical examples cover two study cases for mooring lines belonging to Floating Production Storage and Offloading (FPSO) units installed offshore Brazil. It is shown that the consideration of dependence between peaks leads to lower extreme estimates and that both approaches return accurate results.