A short proof of a conjecture on the TrT_r-choice number of even cycles

In this note we prove that the $T_r$-choice number of the cycle $C_{2n}$ is equal to the $T_r$-choice number of the path (tree) on $4n-1$ vertices, i.e. $T_r$-$ch(C_{2n}) = \left\lfloor(2r+2)(4n-2)/(4n-1)\right\rfloor + 1$. This solves a recent conjecture of Alon and Zaks. \u

Ancestral Caddo Ceramic Vessels from Sites in the Upper Neches River Basin in Anderson and Cherokee Counties, Texas

Late Caddo period sites belonging to the Frankston phase (ca. A.D. 1400-1680) and the Historic Caddo Allen phase (ca. A.D. 1680-1800) are common in the upper Neches River basin in East Texas, including habitation sites as well as associated and unassociated cemeteries. As is well known, ancestral Caddo cemeteries have burial features with associated funerary offerings, most commonly ceramic vessels. In this article, we document 34 ancestral Caddo ceramic vessels in the collections of the Texas Archeological Research Laboratory at The University of Texas at Austin (TARL) from six different sites in the upper Neches River basin, including the Ballard Estates (41AN53, n=4 vessels), O. L. Ellis (41AN54, n=15), Lee Ellis (41AN56, n=1), Dabbs Estate (41AN57, n=3), A. H. Reagor (41CE15, n=3), and John Bragg (41CE23, n=8 vessels) sites. Our first purpose is to put on record these ceramic vessels from six poorly known ancestral Caddo sites in order to better understand the history of Caddo settlement in the upper Neches River basin, including the history of burial interments at these sites. The second purpose is much broader, and is part of an effort to establish an East Texas Caddo ceramic vessel database that can be employed for a variety of research purposes. The synthesis of the stylistically diverse Caddo ceramic wares in different recognized ancestral communities across the Caddo area, including the upper Neches River basin occupied by a Hasinai Caddo group, would seem to be tailor-made for studies of ancestral Caddo social networks and social identities that rely on large regional ceramic datasets. The formal and statistical assessment of the regional variation in Caddo ceramic assemblages is currently being assembled in a Geographic Information System by Robert Z. Selden, Jr. (Stephen F. Austin State University), and the assemblages include the vessels from the six sites discussed herein. This is based on the delineation of temporal and spatial divisions in the character of Caddo ceramics (i.e., principally data on decorative methods, vessel forms, defined types and varieties, and the use of different tempers) across East Texas sites and other parts of the Caddo area, and then constructing networks of similarities between ceramic assemblages from these sites that can be used to assess the strength of cultural and social relationships among Caddo communities in the region through time and across space. The identification of such postulated relationships can then be explored to determine the underlying reasons for the existence of such relationships, including factors such as the frequency of interaction and direct contact between communities, the trade and exchange of ceramic vessels, population movement, and similarities in the organization of ceramic vessel production. In conjunction with a database on 2D/3D-scanned Caddo ceramic vessels from East Texas sites, the East Texas Caddo ceramic vessel database is made part of a digital database where comprehensive mathematical and quantitative analyses of morphological attributes and decorative elements on vessels can be conducted. Queries to such a combined database of vessels and sherds should lead to better understandings of regional Caddo ceramic stylistic and technological attributes and their spatial and temporal underpinnings. The results of past and current instrumental neutron activation analysis (INAA) and petrographic analysis of Caddo Area ceramics, including East Texas (where there is a robust INAA database) can also be explored as a means to corroborate production locales, and establish the chemical and paste characteristics of local fine ware and utility ware ceramics in assemblages of different ages. These in turn allow the evaluation of the possible movement of ceramic vessels between different Caddo communities in East Texas and the broader Caddo world

The generalized work function algorithm is competitive for the generalized 2-server problem

The generalized 2-server problem is an online optimization problem where a sequence of requests has to be served at minimal cost. Requests arrive one by one and need to be served instantly by at least one of two servers. We consider the general model where the cost function of the two servers may be different. Formally, each server moves in its own metric space and a request consists of one point in each metric space. It is served by moving one of the two servers to its request point. Requests have to be served without knowledge of the future requests. The objective is to minimize the total traveled distance. The special case where both servers move on the real line is known as the CNN-problem. We show that the generalized work function algorithm is constant competitive for the generalized 2-server problem

The Generalized Work Function Algorithm Is Competitive for the Generalized 2-Server Problem

The generalized 2-server problem is an online optimization problem where a sequence of requests has to be served at minimal cost. Requests arrive one by one and need to be served instantly by at least one of two servers. We consider the general model where the cost function of the two servers may be different. Formally, each server moves in its own metric space and a request consists of one point in each metric space. It is served by moving one of the two servers to its request point. Requests have to be served without knowledge of future requests. The objective is to minimize the total traveled distance. The special case where both servers move on the real line is known as the CNN problem. We show that the generalized work function algorithm, $\mathrm{WFA}_{\lambda}$, is constant competitive for the generalized 2-server problem. Further, we give an outline for a possible extension to $k\geqslant2$ servers and discuss the applicability of our techniques and of the work function algorithm in general. We conclude with a discussion on several open problems in online optimization

Development of a Hydrodynamic Model for River Sosiani

River Sosiani’s catchment is a sub-catchment of the larger river Nzoia sub-basin which drains into Lake Victoria. River Sosiani drains rich agricultural lands and is the source of water for Eldoret town. The river is also the receiving body of effluent discharges from Eldoret town. It, therefore, has a major economic and environmental value in the western region of Kenya. For effective and sustainable management of river Sosaini it is important, among other things, to understand the hydrology and hydraulics of the river. MIKE 11 HD software was applied to simulate river Sosiani’s discharge. The river’s catchment was delineated from topographical map sheets after digitization using ArcView 3.3 GIS software. Geometrical parameters of the river were obtained by physical survey. In total seventeen cross-sections were surveyed. The model was calibrated using measured streamflow at the catchment outlet for three years and then validated for additional three years. The reliability of the MIKE 11 HD module was evaluated based on the Efficiency Index (EI) and Root Mean Square Error (RMSE). The EI and RMSE obtained are 0.75 and 0.050 m3s-1, respectively. This model can be used for various watershed management purposes, including construction of the river’s water quality model. Keywords: River Sosiani; Hydrodynamic model; MIKE 11; model calibration, model validatio

Non-isothermal, non Newtonian flow of polymers in complex geometries

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