With every (not necessarily abelian) topological group G there is associated a com- pact Hausdorﬀ group bG, the so-called Bohr compactification of G, and a continuous homomorphism b of G onto a dense subgroup of bG such that bG is characterized by the following universal property: given any continuous homomorphism h of G into a **compact** group K, there is always a continuous homomorphism ¯ h of bG into K such that h = ¯ h ◦ b (see [28, V § 4], where a detailed study on bG and their properties is given). In Anzai and Kakutani [3] bG is built when G is **locally** **compact** abelian (LCA). However, most authors agree that it was A. Weil [49] the first to build bG. Weil called bG “Groupe **compact** attach´ e ` a G ”. The name of Bohr compactification was given by Alfsen and Holm [2] in the context of arbitrary topological groups. The Bohr topology of a topological group G is the one that inherits as a subgroup of bG.

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In this paper we prove Conjecture 1 in an important special case, namely, when X is a topological group endowed with the natural action of its **locally** **compact** subgroup G (see Corollary 1.5). We ﬁrst show that X is a proper G-space and then we establish a more general result (Theorem 1.2) which has many interesting applications in the theory of topological groups.

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Remarks 5.4. (i) The reader may have noticed that while Theorem 5.2 is proved for any topological group G, Corollary 5.3 is proved only for **locally** **compact** groups. In fact, Veech’s theorem may fail dramatically at some points of G LUC when G is not **locally** **compact**, as for example when G is extremely amenable. A topological group G is said to be extremely amenable when G LUC has a point which is left invariant, i.e., when there exists x ∈ G LUC such that sx = x for every s ∈ G. Examples of extremely amenable groups, and further details on this interesting theory can be found, for instance, in [17, 27, 42].

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In fact, as we will show, none of this is necessary. The proof of the Plancherel Theorem for R n via Zak transforms uses only basic Fourier series ideas and applies with only syperﬁcial changes in notation to every **locally** **compact**, Abelian group (LCA group).

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Among them, maps that preserve the disjointness of cozeroes defined between spaces of scalar- valued continuous functions on **locally** **compact** and **compact** spaces, as a generalization of the concept of homomorphism, have a long history in functional analysis in the context of rings, algebras, or vector lattices under several names such as Lamperti operators, separating maps, disjointness preserving operators, etc. (see, for example, [1, 2, 3, 4, 5, 7, 8, 13, 16]). In recent years, certain attention has been given to such maps when defined on spaces of vector-valued continuous functions (see, e.g., [10, 14]). However, we do not know much about disjointness preserving maps on vector- valued settings in comparison with scalar-valued contexts and something similar can be said with regard to (algebra) homomorphisms between vector-valued group algebras.

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Since the 40’s, when disjointness preserving mappings began to be used, many authors have studied them on several contexts. Among others, on Ba- nach lattices (see e.g. [1], [2] or [6]), on spaces of continuous functions (see e.g. [14], [3], [7], [15] or [12]), on group algebras of **locally** **compact** Abelian groups ([8]), on Fourier algebras ([10] and [20]) and on some others (see e.g. [16], [17] or [5]).

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An analytical, physics-based and predictive **compact** model for nanoscale multiple-gate junc- tionless and inversion mode MOSFETs was developed in this doctoral study. A new drain current expressions for junctionless MOSFETs was presented, whereby its accuracy was verified from the depletion to the accumulation region. The developed model is valid in all regions of device operation and was proved to predict the electrical behavior of most practical present and future device structures well. The developed model equations are in strong relation to the device physics, whereby the number of adjustable parameters was kept at a minimum level. Throughout the thesis the model was compared versus numerical TCAD simulation data [34] and additionally, in the case of the junctionless triple-gate device, versus measurement data. Several important physical effects were included in the modeling approach in order to keep pace with the strong requirements of the ITRS [21].

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It is evident that the analysis of the transport energy consumption seems to be shadowed by the analysis of the total energy consumption in the residential area. The latter is intersected by the economical variable related to the income of the population and shows a higher consumption in **compact** areas with less mobility. This means that considering energy consumption as the main energy efficiency indicator in certain areas is not enough, so it should be complemented with other factors that contribute to delimiting exact minimun and maximun measurements in both **compact** and diffuse areas. Therefore, modality should be taken into account. High mobility consumption in peripheral areas could be reverted by planning transport systems including rail ways. Furthermore, a higher centralization of activities in those zones could lead to a decreased mobility.

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galaxies. The Cen A objects (solid circles) have parameters derived in this work. Local Group GC data (open diamonds) were taken from McLaughlin & van der Marel (2005) for LMC, SMC, MW clusters, while the early-type galaxy data (open triangles) were culled from Bender et al. (1992). The dE/dE,N/core data (asterisks) were taken from Geha et al. (2002). The UCD data (open squares) are from three sources: Virgo UCDs are taken from Evstigneeva et al. (2007), and Fornax UCDs from Mieske et al. (2008) and Patrick Cˆot´e (2009, private communication). Several interesting **compact** stellar systems are labeled. Dotted and solid curves are exponential and power-law fits, respectively, as described in Section 4.2. Dotted lines indicate the mass break of Ha¸segan et al. (2005) at M dyn 2 × 10 6 M and typical luminosities for UCDs in the range − 13.5 mag < M V < − 11.5 mag from Hilker (2009).

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Key tools in harmonic analysis and numerical application are the Rellich’s the- orem and the **compact** trace theorem. This paper deals with the **compact** trace theorem in domains Ω ⊂ R 3 with external cusps. We show that if the power sharpness α of the cusp is bellow a critical exponent α c , then the trace operator

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Much effort in Green Computing has been devoted to pro- moting a wise usage of the resources and improving energy consumptions of hardware components or IT infrastructures. However, the industry road map needs to move its efforts to finding solutions in Green Software [50]. Instead of mak- ing better chips, the focus will be centered in the different applications developed for smartphones, supercomputers, or even data centers in the cloud. Then, after understanding what these efficient high-level applications require, it will be possible to go down to develop the chips and hardware to support their needs. Research in Green Software is therefore gaining more attention, especially in the areas of quality and design/construction, followed by requirements [9]. Moreover, computing is not defined any more by the needs of traditional PCs or data centers. Today, many people live surrounded by multiple mobile computing devices, such as smartphones, tablets, wearables, smart TVs, smart home products, and other kinds of sensors and IoT devices. In this scenario, energy efficient software is of extreme importance, as it can save battery and reduce the heat generated in the devices, which in turns increases the speed and longevity of these mobile devices. Green IoT has emerged as a field of research to tackle this problem, proposing generally hardware-based approaches, in addition to other efforts that can be categorized as software-based, habitual-based, awareness-based, policy- based, or recycling-based [51]; however, approaches using **compact** data structure have not been used in this context up to now.

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Abstract. Given an instance of an optimization problem together with an optimal solution, we consider the scenario in which this instance is modified **locally**. In graph problems, e. g., a singular edge might be removed or added, or an edge weight might be varied, etc. For a problem U and such a local modification operation, let lm- U (local-modification- U ) denote the resulting problem. The question is whether it is possible to exploit the additional knowledge of an optimal solution to the original instance or not, i. e., whether lm- U is computationally more tractable than U . Here, we give non-trivial examples both of problems where this is and problems where this is not the case. Our main results are these: 1. The local modification to change the cost of a singular edge turns the traveling salesperson problem ( TSP ) into a problem lm-TSP which is as hard as TSP itself, i. e., unless P = N P , there is no polynomial-time p(n)-approximation algorithm for lm-TSP for any polynomial p. Moreover, lm-TSP where inputs must satisfy the β- triangle inequality ( lm- ∆ β -TSP ) remains NP-hard for all β > 1

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In this paper we have presented the spectroscopic analysis of four ultra-**compact** dwarf galaxies (UCDs) and one nucleus of a dwarf elliptical. These UCDs are among the five brightest in the central region of the Fornax cluster (Hilker et al. 1999b; Drinkwater et al. 2003). The analysis is based on high resolution spectra obtained with the instrument UVES mounted in the VLT at El Paranal, Chile. Velocity dispersions were derived from selected wavelength regions using the direct-fitting method by van der Marel (van der Marel & Franx 1993). To derive the masses of the UCDs a new modelling program has been devel- oped that allows to choose between diﬀerent representations of the surface brightness profile (i.e. Nuker, Sersic or King laws) and corrects the observed velocity dispersions for observational parameters (i.e. seeing, slit size). The light profile parameters of the UCDs and the nucleus of FCC 303 were obtained from Hubble Space Telescope imaging (see the accompanying paper by Evstigneeva et al. 2006). The derived dynamical masses then have been compared to those expected from stellar population models. The main results of our analysis are as follows:

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Steenrod [13] for the standard product but with a different function space. In it one takes CH maps instead of continuous maps and "Haussdorff-**compact** open" topology instead of "**compact** open" topology. Then one defines a retract of this category where the retraction functors are both right and left adjoint of each other and define in fact an equivalence of categories. Therefore all the categorical properties of the original one are functorially transmitted to the second.

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El **Compact** Framework, en respuesta a la segunda interrogante, provee mecanismos para el acceso remoto a datos a través de una lista de clases. Algunas clases de hallan en el espacio de nombre System.Data.SqlClient (cliente de SQL). Este espacio contiene clases para establecer la conexión, obten- ción de permisos de acceso, manejo de condiciones de error o no disponibilidad, realización de consultas, actualizaciones, transacciones, etc. En la sección previa de «Uso Arrays y Tablas» se expusieron clases que permiten el modelado de contenedores de información fuera de línea (offline). Estos contenedores, también llamados caché, pueden emplearse para alojar la información recuperada a través de una conexión remota. El proceso de acceso a datos implica que una cantidad de información es conducida al dispositivo móvil. La aplicación puede usar la información para realizar consultas simplemente, o puede introducir cambios que necesitarán ser actualizados en el servidor central. Durante los períodos de desconexión, se accede a los datos del caché.

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Las conexiones de los auxiliares salen del **Compact** a través de los bloques de conexión, de 3 o 6 bornes según el auxiliar a conectar. Estos bloques incorporan bornes numerados y están compuestos : c una parte móvil, fijada en el **Compact**, y que se conecta con las conexiones internas. Estas conexiones están identificadas por hilos de colores; c una parte fija, montada en el zócalo o en el chasis. Esta parte fija que constituye la regleta de bornes terminal, conecta directamente con las conexiones exteriores (lengüetas de 6,35 mm).

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**Locally** Recoverable (LRC) Error-Correcting codes were introduced in [6] motivated by the recent and significant use of coding techniques applied to distributed and cloud storage systems. Roughly speaking, local recovery techniques enable us to repair lost encoded data by a ”local procedure”, which means by making use of small amount of data instead of all information contained in a codeword.

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‘k_write_strobe’ - This output can be left open as it is associated with 16 additional ‘constant optimized ports’ that have their own ‘OUTPUTK’ instruction.The normal input and output ports associated with ‘read-Strobe’ and ‘write_strobe’ will all behave exactly the same as they did previously. Many PicoBlaze users have expressed their desire for a PicoBlaze that can write constant values directly to a port so KCPSM6 can and you can read more on pages 75 to 80. ‘bram_enable’ – This is purely a power reduction feature and failure to connect it will have no effect on the execution of a program providing the BRAM containing the program is **locally** enabled. So if you want to continue using your existing ‘ROM_form’ templates you can but it probably is worth making the small adjustment to include the enable since it is virtually free to do so and will save some power (every little helps!). Given the move to Spartan-6 or Virtex-6 is if generally better for you to adopt the new program memory templates where you will find the enable input waiting to be connected (and ‘rdl’). See page 8. Address[11:10] – So this is the one you probably do need to look at because it means that KCPSM6 can support programs up to 4K. The address port is 12- bits rather than the 10-bit address port of KCPSM3. Of course this means that any KCPSM3 programs will continue to fit in 1K and only the lower 10-bits of the address will really be used in these situations. Whilst address[11:10] are redundant until you implement larger programs, the new program memory templates always connect all 12-bits to make design easy and facilitate easy when required. Please see pages 8 to 13 to see how easy and flexible this is! New Generics – KCPSM6 has 3 generics (KCPSM3 didn’t have any!). The three generics enable you to increase the size of the scratch pad memory, define an interrupt vector address of your choice and define a hardware build value. However, the default settings result in an identical implementation to KCPSM3 meaning that you will have 64 bytes of scratch pad memory and the interrupt vector will be address ‘3FF’. The hardware build value is associated with a new instruction so will have no effect on code imported from a KCPSM3 design. Put simply, you can ignore the generics until you read page 34.

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3.2. Prediction of Response Based on Microarrays of Gene Expression in Peripheral Blood. Peripheral blood mononu- clear cells have emerged recently as pathology markers of cancer and other diseases, making their use as therapy predictors possible. Furthermore, the importance of the immune response in radiosensitivity of solid organs led Palma et al. [8] to hypothesize that microarray gene expres- sion profiling of peripheral blood mononuclear cells could identify patients with response to CRT in LARC. Thirty- five 35 patients with **locally** advanced rectal cancer were recruited initially to perform the study. Peripheral blood samples were obtained before neoadjuvant treatment. RNA was extracted and purified to obtain cDNA and cRNA for hybridization of microarrays included in Human WG CodeLink bioarrays. Quantitative real-time PCR was used to validate microarray experiment data. Results were correlated with pathological response, according to Mandard’s criteria and final UICC Stage (patients with tumor regression grades 1-2 and downstaging being defined as responders and patients with grades 3–5 and no downstaging as nonresponders). The authors performed a multiple 𝑡-test using Significance Analysis of Microarrays to find those genes differing sig- nificantly in expression between responders (𝑛 = 11) and nonresponders (𝑛 = 16) to CRT. The differently expressed genes were BC 035656.1, CIR, PRDM2, CAPG, FALZ, HLA- DPB2, NUPL2, and ZFP36. The measurement of FALZ (𝑃 = 0.029) gene expression level determined by qRT-PCR showed statistically significant differences between the two groups. They postulated the idea that gene expression profiling reveals novel genes in peripheral blood samples of mononuclear cells that could predict responders and nonresponders to CRT in patients with LARC. The authors hypothesized the importance of mononuclear cells’ mediated response in the neoadjuvant treatment of rectal cancer.

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member galaxies have been critical to our understanding of galaxy formation and evolution in dense environments, and provide a local benchmark for comparative studies of galaxy evolution in different environments and at higher redshift (e.g., the morphology-density relation and the Butcher-Oemler effect; Dressler 1980; Butcher & Oemler 1984). However, the properties of intrinsically faint ob- jects in the Coma cluster are not yet well characterized compared to other local clusters such as Virgo and For- nax. The resolution and sensitivity afforded by the Hub- ble Space Telescope-Advanced Camera for Surveys (HST- ACS; Ford et al. 1998) has allowed for detailed studies of faint and **compact** systems in Coma (Carter et al. 2008, hereafter Paper I), such as measuring the structural pa- rameters of dwarf galaxies (C. Hoyos et al. 2010, submit- ted, hereafter Paper III), constraining the globular clus- ter (GC) population (E. Peng et al. 2010, submitted, here- after Paper IV), studying the nature of **compact** elliptical galaxies (Price et al. 2009, hereafter Paper V) and ultra- **compact** dwarf galaxies (UCDs; K. Chiboucas et al. 2011, in prep), and establishing membership for faint cluster member galaxies by morphology (Chiboucas et al. 2010). The ACS Coma Cluster Treasury survey was initiated in HST Cycle 15 following the success of the ACS cluster surveys performed in Virgo (Cˆ ot´e et al. 2004) and For- nax (Jord´an et al. 2007). In contrast to the Virgo and Fornax surveys that targeted individual early-type galax- ies, the Coma fields were arranged to maximize spatial coverage at the cluster core as well as provide targeted observations at an off-center region of Coma. The ad- vantage of this observing strategy is that it allows for statistical measurements of faint cluster members (e.g., the luminosity function (LF); N. Trentham et al. 2011, in prep, hereafter Paper VI) while also probing the ef- fects of the cluster environment across a wide range of cluster-centric distance. Although the Coma cluster is

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