$${\varvec{\mathcal {}}}$$-minimaxness and local cohomology modules

Let R be a commutative Noetherian ring, \({\mathfrak {a}}\) an ideal of R, M a finitely generated R-module, and \({\mathcal {S}}\) a Serre subcategory of the category of R-modules. We introduce the concept of \({\mathcal {S}}\)-minimax R-modules and the notion of the \({\mathcal {S}}\)-finiteness dimension

$$\begin{aligned} f_{\mathfrak {a}}^{{\mathcal {S}}}(M):=\inf \lbrace f_{\mathfrak {a}R_{\mathfrak {p}}}(M_{\mathfrak {p}}) \vert \mathfrak {p}\in {\text {Supp}}_R(M/ \mathfrak {a}M) \text { and } R/\mathfrak {p}\notin {\mathcal {S}} \rbrace \end{aligned}$$

and we will prove that: (i) If \({\text {H}}_{\mathfrak {a}}^{0}(M), \cdots ,{\text {H}}_{\mathfrak {a}}^{n-1}(M)\) are \({\mathcal {S}}\)-minimax, then the set \(\lbrace \mathfrak {p}\in {\text {Ass}}_R( {\text {H}}_{\mathfrak {a}}^{n}(M)) \vert R/\mathfrak {p}\notin {\mathcal {S}}\rbrace \) is finite. This generalizes the main results of Brodmann–Lashgari (Proc Am Math Soc 128(10):2851–2853, 2000), Quy (Proc Am Math Soc 138:1965–1968, 2010), Bahmanpour–Naghipour (Proc Math Soc 136:2359–2363, 2008), Asadollahi–Naghipour (Commun Algebra 43:953–958, 2015), and Mehrvarz et al. (Commun Algebra 43:4860–4872, 2015). (ii) If \({\mathcal {S}}\) satisfies the condition \(C_{\mathfrak {a}}\), then

$$\begin{aligned} f_{\mathfrak {a}}^{{\mathcal {S}}}(M)= \inf \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not } {\mathcal {S}}\hbox {-}minimax\rbrace . \end{aligned}$$

This is a formulation of Faltings’ Local-global principle for the \({\mathcal {S}}\)-minimax local cohomology modules. (iii) \( \sup \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not } {\mathcal {S}}\text {-minimax} \rbrace = \sup \lbrace i\in {\mathbb {N}}_{0} \vert {\text {H}}_{\mathfrak {a}}^{i}(M) \text { is not in } {\mathcal {S}} \rbrace \).

     

Spectrophotometric determination of aqueous acidity constants of three azo dyes

The two successive steps acidity constants of three azo dye derivatives D1–D3, were determined by a spectrophotometric method using 0.10 M KNO₃ as supporting electrolyte in water solvent. The electronic spectra of the compounds were recorded in the course of their pH-metric titration with a standard base solution. The protolytic equilibrium constants can be solved very satisfactorily from absorbance data, by combining the data obtained in the spectrometric determinations with graphic methods as the absorbance diagrams. An A-diagram shows the relative absorbance changes at two wavelengths as a function of the pH. For a one-step system, the absorbance at any wavelength must be proportional to the absorbance at any other wavelength, so an A-diagram for all wavelength combinations for such a system must be linear (rank, s=1). However, if a system is governed by two or more equilibria, the A-diagrams corresponding to multi-step titrations will change direction every time a new equilibrium becomes dominant in the system. Analysis of the each uniform sub-region can then be used in evaluating of the corresponding equilibrium. A-diagrams for all wavelength combinations suggest that these systems have the rank two(s=2). The results revealed that the K_a(1) and K_a(2) values of different azo dyes follow the order D3>D2>D1.      

Microwave Assisted,Solvent Free One Pot Synthesis of Nitriles from Aryl Aldehydes on Melamin Formaldehyde as Solid Support

Various aryl aldehydes underwent prompt one pot conversion into the corresponding nitriles in high yields by reacting with hydroxylamine hydrochloride supported on melamine formaldehyde under microwave irradiation in the presence of ammonium acetate as catalyst.     

Gain enhancement in two-stream free electron laser with planar wiggler and axial guide magnetic field

The theory for the two-stream free electron laser (FEL) consisting of a relativistic electron beam transported along the axis of a planar wiggler in the presence of an axial guiding magnetic field is proposed and investigated. The electron trajectories and the small signal gain are derived. The characteristic of the linear gain and the normalized maximum gain are studied numerically. The result shows that the normalized maximum gain is considerably enhanced in comparison with that of the single stream. The effect of the difference between the energies of the two beams in this configuration of FEL is also considered, and we find that the gain is affected by the energy differences between groups 1 and 2.     

Modules Whose t-Closed Submodules Have a Summand as a Complement

We define and investigate T ₁₁-type modules as a generalization of t-extending modules, and modules satisfying C ₁₁ condition. A module M is said to be T ₁₁-type if every t-closed submodule of M has a complement which is a direct summand. Direct sums of T ₁₁-type modules inherit the property. Some equivalent conditions for a module M to be T ₁₁-type are given. We characterize a module M for which every direct summand satisfies T ₁₁ condition. If R _R is T ₁₁-type, then R/Z ₂(R _R ) is a C ₂ ring if and only if it is a von Neumann regular ring. Applying this result, we characterize a right t-extending (resp., finitely Σ-t-extending, or Σ-t-extending) ring R for which R/Z ₂(R _R ) is von Neumann regular.     

Transport and Energy Deposition of hot Electrons through the Shock Ignition pre Compressed Target

Shock ignition as an alternative scheme of the laser fusion has the potential of achieving efficient implosion. However, hot electrons produced in result of ignitor‐corona interaction may penetrate deep into the fuel making the compression less effective. Transport and energy deposition of hot electron beam into the dense pre compressed of HiPER target by means of Monte Carlo approach are discussed considering the influence of real density and electron beam characteristics. The target parameters before igniting the hot spot have been extracted from a fluid code and used as the initial profile for Monte Carlo simulations. In comparison with simplified step like density profile, electrons penetrate slightly deeper in the case of real shaped density profile. In addition, deposition zone of a broad spectrum electron beam is wider while, monoenergetic electrons depose their energy locally resulting more maximum energy deposition value. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pt(II) complexes immobilized on polymer‐modified magnetic carbon nanotubes as a new platinum drug delivery system

We combine nanotechnology and chemical synthesis to create a novel multifunctional platinum drug delivery vehicle based on magnetic carbon nanotubes (multiwall carbon nanotubes/Fe₃O₄@poly(citric acid)/cis‐[(Pt(1,7‐phenanthroline)(DMSO)Cl₂)]‐b‐poly(ethylene glycol) (MCNTs/FO@PC/Pt(II)‐b‐PEG)) for targeted cancer therapy. MCNTs/FO@PC/Pt(II)‐b‐PEG was conveniently prepared by conjugating cis‐[Pt(1,7‐phenanthroline)(DMSO)Cl₂] complex to MCNTs/FO@PC‐b‐PEG via strong hydrogen‐bonding interactions. In comparison with free cisplatin and Pt(II) complex, MCNTs/FO@PC/Pt(II)‐b‐PEG shows higher solubility in aqueous solution and higher cytotoxicity towards human cervical cancer HeLa cells and human breast cancer MDA‐MB‐231 cells. In vitro release experiments revealed that the platinum drug‐loaded delivery system is relatively stable under physiological conditions (pH = 7.4 and 37 °C) but susceptible to acidic environments (pH = 5.6 and 37 °C) which would trigger the release of loaded drugs. Fluorescence microscopy studies revealed that this magnetic nanohybrid system possesses marked cell‐specific targeting in vitro in the presence of an external magnetic field. The results indicated that the prepared superparamagnetic MCNTs/FO@PC/Pt(II)‐b‐PEG nanohybrid system is a promising candidate for inhibiting the proliferation of cancer cells.     

A heuristic method to schedule training programs for Small and Medium Enterprises

During the life period of Small and Medium Enterprises (SMEs) in incubators they need some training programs to acquire the required knowledge in order to survive and succeed in the business environment. This paper presents a heuristic method based on an optimization model to schedule these programs at the most suitable times. Based on the proposed heuristic, each training program is implemented in a suitable time by considering the SMEs’ requirements and some other logical constraints. The proposed heuristic is described in detail, and its implementation is demonstrated via a real-life numerical example. The numerical results of the heuristic are compared with other methods.     

The Exterior Degree of a Pair of Finite Groups

The exterior degree of a pair of finite groups (G, N), which is a generalization of the exterior degree of finite groups, is the probability for two elements (g, n) in (G, N) such that g ? n = 1. In the present paper, we state some relations between this concept and the relative commutatively degree, capability and the Schur multiplier of a pair of groups.     

Multi-criteria supplier segmentation using a fuzzy preference relations based AHP

One of the strategic activities of a firm is supplier segmentation, whereby a firm creates groups of suppliers to handle them differently. Existing literature provides several typologies of suppliers, each of which uses different dimensions/variables. In this paper, different typologies are combined by distinguishing two overarching dimensions, the capabilities and the willingness of suppliers to cooperate with a particular firm. These dimensions cover almost all the existing supplier segmentation criteria mentioned in existing literature. For each particular situation, these dimensions can be specified using a multi-criteria decision-making method. A methodology is proposed that includes a fuzzy Analytic Hierarchy Process (AHP) which uses fuzzy preference relations to incorporate the ambiguities and uncertainties that usually exist in human judgment. The proposed methodology is used to segment the suppliers of a broiler company. The result is a segmentation of suppliers based on two aggregated dimensions. Finally some strategies to handle different segments are discussed and concluding remarks and suggestions for future research are provided.