Fuzzy linear regression and its applications to forecasting in uncertain environment

Linear regression has been used for many years in developing mathematical models for application in marketing, management, and sales forecasting. In this paper, two different sales forecasting techniques are discussed. The first technique involves non-fuzzy abstract methods of linear regression and econometrics. A study of the international market sales of cameras, done in 1968 by John Scott Armstrong, utilized these non-fuzzy forecasting techniques. The second sales forecasting technique uses fuzzy linear regression introduced by H. Tanaka, S. Uejima, and K. Asai, in 1980. In this paper, a study of the computer and peripheral equipment sales in the United States is discussed using fuzzy linear regression. Moreover, fuzzy linear regression is applied to forecasting in an uncertain environment. Finally, some possible improvements and suggestions for further study are mentioned.     

Uniform-cost inverse absolute and vertex center location problems with edge length variations on trees

This article considers the inverse absolute and the inverse vertex 1-center location problems with uniform cost coefficients on a tree network T with n+1 vertices. The aim is to change (increase or reduce) the edge lengths at minimum total cost with respect to given modification bounds such that a prespecified vertex s becomes an absolute (or a vertex) 1-center under the new edge lengths. First an O(nlogn) time method for solving the height balancing problem with uniform costs is described. In this problem the height of two given rooted trees is equalized by decreasing the height of one tree and increasing the height of the second rooted tree at minimum cost. Using this result a combinatorial O(nlogn) time algorithm is designed for the uniform-cost inverse absolute 1-center location problem on tree T. Finally, the uniform-cost inverse vertex 1-center location problem on T is investigated. It is shown that the problem can be solved in O(nlogn) time if all modified edge lengths remain positive. Dropping this condition, the general model can be solved in O(r_vnlogn) time where the parameter r_v is bounded by ⌈n/2⌉. This corrects an earlier result of Yang and Zhang.     

On the existence of 3-way k-homogeneous Latin trades

A $\mu$-way Latin trade of volume $s$ is a collection of $\mu$ partial Latin squares $T_1,T_2,\dots ,T_{\mu }$, containing exactly the same $s$ filled cells, such that, if cell $(i,j)$ is filled, it contains a different entry in each of the $\mu$ partial Latin squares, and such that row $i$ in each of the $\mu$ partial Latin squares contains, set-wise, the same symbols, and column $j$ likewise. It is called a $\mu$-way$k$-homogeneous Latin trade if, in each row and each column, $T_r$, for $1\le r\le \mu$, contains exactly $k$ elements, and each element appears in $T_r$ exactly $k$ times. It is also denoted as a $(\mu ,k,m)$ Latin trade, where $m$ is the size of the partial Latin squares.We introduce some general constructions for $\mu$-way $k$-homogeneous Latin trades, and specifically show that, for all $k\le m$, $6\le k\le 13$, and $k=15$, and for all $k\le m$, $k=4,5$ (except for four specific values), a $3$-way $k$-homogeneous Latin trade of volume $km$ exists. We also show that there is no $(3,4,6)$ Latin trade and there is no $(3,4,7)$ Latin trade. Finally, we present general results on the existence of $3$-way $k$-homogeneous Latin trades for some modulo classes of $m$.     

Latent ruthenium initiators containing fluoro aryloxide ligands

A new ligand, methyl 2,3,5,6-tetrafluoro-4-oxybenzoate (C₈H₃F₄O₃), combining an electron withdrawing group (C₆F₄) to tune the reactivity with an anchor group (CO₂Me) for immobilization on supports, was used to prepare four new ruthenium initiators, viz. Ru(C₈H₃F₄O₃)₂(CHPh)(3-Br-C₅H₅N)(H₂IMes) and Ru(C₈H₃F₄O₃)₂XL, where X = C,N-(CHCH₂CH₂-2-C₅H₄N) and L = PⁱPr₃, PCy₃ or H₂IMes. The new ligand greatly reduced the reactivity of the ruthenium centre at room temperature. The ¹H NMR and DSC investigation for the ROMP of norbornene dicarboximide monomers clearly demonstrated that the Ru(C₈H₃F₄O₃)₂XL initiators were inactive at room temperature and required elevated temperatures for their activation.     

Efficient Synthesis of 3-Pyrrolin-2-one Derivatives in Aqueous Media

An efficient one-pot, three-component synthesis of 3-pyrrolin-2-ones in aqueous media at room temperature is reported. This reaction provides a green and catalyst-free method for generation of 3-pyrrolin-2-one derivatives in good yields.     

Microwave‐Assisted Aromatization of 1,3,5‐Trisubstituted 2‐Pyrazolines by Bi(NO3)3 · 5H2O,as a Novel and Convenient Oxidizing Agent

Abstract

Bismuth(III) nitrate pentahydrate, Bi(NO₃)₃?·?5H₂O, has been used as a mild, efficient, and inexpensive oxidant for the oxidative aromatization of several 1,3,5‐trisubstituted 2‐pyrazolines to pyrazoles in acetic acid under microwave irradiation with good to excellent yields.     

Thermal Degradation Kinetics and Modeling Study of Ultra High Molecular Weight Polyethylene (UHMWP)/Graphene Nanocomposite

The incorporation of nanofillers such as graphene into polymers has shown significant improvements in mechanical characteristics, thermal stability, and conductivity of resulting polymeric nanocomposites. To this aim, the influence of incorporation of graphene nanosheets into ultra-high molecular weight polyethylene (UHMWPE) on the thermal behavior and degradation kinetics of UHMWPE/graphene nanocomposites was investigated. Scanning electron microscopy (SEM) analysis revealed that graphene nanosheets were uniformly spread throughout the UHMWPE’s molecular chains. X-Ray Diffraction (XRD) data posited that the morphology of dispersed graphene sheets in UHMWPE was exfoliated. Non-isothermal differential scanning calorimetry (DSC) studies identified a more pronounced increase in melting temperatures and latent heat of fusions in nanocomposites compared to UHMWPE at lower concentrations of graphene. Thermogravimetric analysis (TGA) and derivative thermogravimetric (DTG) revealed that UHMWPE’s thermal stability has been improved via incorporating graphene nanosheets. Further, degradation kinetics of neat polymer and nanocomposites have been modeled using equations such as Friedman, Ozawa–Flynn–Wall (OFW), Kissinger, and Augis and Bennett’s. The "Model-Fitting Method” showed that the auto-catalytic nth-order mechanism provided a highly consistent and appropriate fit to describe the degradation mechanism of UHMWPE and its graphene nanocomposites. In addition, the calculated activation energy (E_a) of thermal degradation was enhanced by an increase in graphene concentration up to 2.1 wt.%, followed by a decrease in higher graphene content.     

Automated Deconvolution of Overlapped Ion Mobility Profiles

Presence of unresolved ion mobility (IM) profiles limits the efficient utilization of IM mass spectrometry (IM-MS) systems for isomer differentiation. Here, we introduce an automated ion mobility deconvolution (AIMD) computer software for streamlined deconvolution of overlapped IM-MS profiles. AIMD is based on a previously reported post-IM/collision-induced dissociation (CID) deconvolution approach [J. Am. Soc. Mass Spectrom. 23, 1873 (2012)] and, unlike the previously reported manual approach, it does not require resampling of post-IM/CID data. A novel data preprocessing approach is utilized to improve the accuracy and efficiency of the deconvolution process. Results from AIMD analysis of overlapped IM profiles of data from (1) Waters Synapt G1 for a binary mixture of isomeric peptides (amino acid sequences: GRGDS and SDGRG) and (2) Waters Synapt G2-S for a binary mixture of isomeric trisaccharides (raffinose and isomaltotriose) are presented. Graphical Abstract

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An exact analytical solution for creeping Dean flow of Bingham plastics through curved rectangular ducts

In this paper, an exact analytical solution for creeping flow of Bingham plastic fluid passing through curved rectangular ducts is presented for the first time. The closed form of axial velocity distribution, flow resistance ratio, and wall shear stress are derived using bounded Fourier transformation. An extensive investigation on mutual effects of Hedstrom number, curvature ratio, and aspect ratio is conducted. The results indicate that a drag reduction is caused in the flow field by increasing the Hedstrom number. It is shown that unlike the Newtonian creeping Dean flow, the critical aspect ratio (an aspect ratio in which the flow resistance ratio is independent from curvature ratio) does not exist at large enough Hedstrom numbers. Analytical solution also indicated that as Hedstrom number is increased, the value of Poiseuille number is enhanced, and unlike the Newtonian flows, the value of Poiseuille number is not zero at edges of cross section.