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# Sphere inscribed in cube of side Radius of sphere is

## THIẾT KẾ TRÊN MÁY VI TÍNH PHẦN 1 AUTOCAD 3D CHƯƠNG 3 PPT

Specify rotation angle of wedge about the Z axis: góc quay chung quanh tr ụ c song song v ớ i tr ụ c z vă tr ụ c năy đ i qua đ i ể m Corner of wedge Ví d ụ : Command: 3D↵ Enter an option[Box/Cone/DIsh/DOme/Mesh/Pyramid/ Sphere/Torus/Wedge]: w↵ Specify corner point of wedge: ch ỉ m ộ t đ i ể m trín măn hình
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## ĐỀ TÀI THE KISSING NUMBER IN FOUR DIMENSIONS PDF

for n = 4, m ≤ 6. Note that Theorem 5 gives for computation of h m a low-dimensional optimization problem (see 5-F ). Our ﬁrst approach for this problem was to apply numerical methods [25]. However, that is a noncon- vex constrained optimization problem. In this case, the Nelder-Mead simplex method and other local improvements cannot guarantee ﬁnding a global op- timum. It is possible (using estimations of derivatives) to organize the com- putational process in such way that it gives a global optimum. However, such solutions are very hard to verify and some mathematicians do not accept that kind of proof. Fortunately, using a geometric approach, estimations of h m can be reduced to relatively simple computations.
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## HIGH TEMPERATURE STRAIN OF METALS AND ALLOYS PART 2 PPTX

A key to the problem is the response of the structural elements of a material. In some way the situation is in accordance with the Le Chatelier rule. The changes in a metallic system which take place under the influence of external conditions are directed so as to relax this influence. The formation of an ordered dislocation structure is just an evolution process which tries to act against applied stresses. The point is that the high temperature conditions give the possibility of supplying the dislocation rearrangement with energy and which results in the substructure formation.
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## THE CAMBRIDGE HISTORY OF THE ENGLISH LANGUAGE VOLUME 3 PART 4 PPSX

In the present chapter, I have attempted to discuss the most important syntactic constructions in Early Modern English, with particular attention to the features which underwent major changes. As mentioned above, the roots of these can be found in Middle or even Old English; in the Modern period, transitional stages were followed by the establishment of the system. The most dramatic developments are connected with verb syntax: the auxiliaries indicating future or (plu)perfect, the progressive ( be ⫹ -ing) and do-periphrasis. In the formation of noun phrases, the use of the arti- cles becomes more systematic than in Middle English, and the possibility of using adjectives or the adjectival forms of inde fi nite pronouns as heads more restricted. Subject–verb order is established in statements, and imper- sonal constructions with no ‘nominative’ subject disappear. At the level of the composite sentence, the distinction between coordination and subor- dination becomes more clearcut than in Middle English and that between the personal relative link who and the impersonal which becomes fi xed. There are, in fact, very few major syntactic changes after the end of the eighteenth century, although change in language is of course an ongoing and never-ending process. The passive of the progressive (the type ‘The house is being built’ instead of the older ‘The house is building’) is prob- ably the most conspicuous of these.
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## Sphere-forming culture enriches liver cancer stem cells and reveals Stearoyl-CoA desaturase 1 as a potential therapeutic target

The role of sphere-forming culture in enriching subpopulations with stem-cell properties in hepatocellular carcinoma (HCC) is unclear. The present study investigates its value in enriching cancer stem cells (CSCs) subpopulations and the mechanism by which HCC CSCs are maintained.
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## BÁO CÁO TOÁN HỌC LOWER BOUNDS FOR THE FOOTBALL POOL PROBLEM FOR 7 AND 8 MATCHES PDF

Submitted: Oct 26, 2006; Accepted: Mar 15, 2007; Published: Mar 28, 2007 Mathematics Subject Classifications: 94B65 Abstract Let k 3 ( n ) denote the minimal cardinality of a ternary code of length n and covering radius one. In this paper we show k 3 (7) ≥ 156 and k 3 (8) ≥ 402 improving on the best previously known bounds k 3 (7) ≥ 153 and k 3 (8) ≥ 398. The proofs are founded on a recent technique of the author for dealing with systems of linear inequalities satisfied by the number of elements of a covering code, that lie in k - dimensional subspaces of F n
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## SAT MATH ESSENTIALS PART 11 PPSX

160 = 16h h = 10 The length of an edge of the cube is equal to half the height of the cylinder. The edge of the cube is 5 units. The surface area of a cube is equal to 6e 2 , where e is the length of an edge of the cube. The surface area of the cube = 6(5) 2 = 6(25) = 150 square units.
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## THE OXFORD COMPANION TO PHILOSOPHY PART 6 PPSX

completely free and individuals enter them only for their own reasons and beneﬁt. Leo Tolstoy (1828–1910), another somewhat atypical anarchist, adopted a type of religious anarchism, using the Bible to attack the rule of one person over another and the legitimacy of secular power. He ﬁnds in the Gospels a doctrine of peace and love that is sufﬁcient for the organization of society and that is violated by governments, laws, police, armies, and private property. Proudhon’s anarchism advocated a soci- ety based on small enterprises and skilled craftsmen who organized to form a co-operative community of equals. Michael Bakunin (1814–76), who favoured violent over- throw of the state, envisaged replacing it with a federation built from below on the basis of voluntary associations. Anarcho-syndicalism focused on trade unions, or syndi- cates, as the engine of change in society, for syndicates championed the interests of the workers and could serve as the basis for social organization after a successful revo- lution had overthrown the existing state structures. Peter Kropotkin (1842– 1921), as an anarcho-communist, held that the individual is essentially a social being who can fully develop only in a communist-type society, which precluded authoritarian rule and the special interests of dominant groups. Like other communists he advocated the abolition of private property and the development of a society built on common ownership of the means of pro- duction. For him the commune is the basic social unit, and communal needs are balanced with individual needs.
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## Handbook of Machine Design P57

where Z is called the section modulus. Equations (49.30) can also be used for beams having unsymmetrical sections provided that the plane of bending coincides with one of the two principal axes of the section. When shear forces are present, as in Fig. 49.6c, a member in flexure will also
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## Sổ tay tiêu chuẩn thiết kế máy P57 pptx

FIGURE 49.3 (a) General triaxial stress element; (b) Mohr's circles for triaxial stress. T — T T — T T — T ^xy ^yx ^yz *zy ^zx ^xz Note that the first subscript is the coordinate normal to the element face, and the second subscript designates the axis parallel to the shear-stress component. The neg- ative faces of the element will have shear stresses acting in the opposite direction; these are also considered as positive.
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## FIBER OPTICS ILLUSTRATED DICTIONARY PART 36 PPSX

facsimile switch An external switching device that allows a single phone line to be used for more than one phone-related piece of equipment. Fax switches often can also handle telephone answering machines and computer modems. The fax switch is attached between the phone line plug and the various phone devices. When a call comes through, the device evalu- ates the tones and decides whether it's a voice call, a modem call, or a fax call, and routes the call to the appropriate device. Unfortunately, most fax switches can't detect when a manual fax machine is going to send a fax if the call originated as a voice call. If the person dials the phone manually and then wants to switch over to a fax call after the connection is es- tablished, many fax switches can't revert to data mode (newer ones may be switchable on receiving a par- ticular code). In spite of that limitation, it's a great tool for homes, home offices, and small businesses that can't afford extra phone lines.
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## SAT II MATH EPISODE 2 PART 8 PDF

46. The correct answer is (A). Equation of an ellipse 47. The correct answer is (B). When x ≥ 2, y = x – 2 + 2; or the straight line y = x . When x < 2, y = 2 – x + 2 = 4 – x , which graphs as another straight line. Thus the graph is a pair of rays that form a “V.”
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## MASTER GMAT 2010 PART 31 DOC

determine altitude (a), draw a vertical line segment connecting point A to BC, which creates a 45°-45°-90° triangle. The ratio of the triangle’s hypotenuse to each leg is = 2:1. The hypotenuse AB 5 2. Thus, the altitude (a) of ABCD is 2 = 2 , or = 2. Accordingly, the area of
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## BÁO CÁO HÓA HỌC:" RESEARCH ARTICLE THE RELATIONAL TRANSLATORS OF THE HYPERSPHERICAL FUNCTIONAL MATRIX" PPTX

P D C TRANG 8 TRANG 9 • • • • TRANG 10 Journal of Chemical Physics Scientic American Sphere Packings, Lattices and Groups Grundlehren der Mathematischen Wissenschaften Journal of Geometr[r]
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## ELECTROMAGNETIC FIELD THEORY: A PROBLEM SOLVING APPROACH PART 75 PDF

R., 201 Time constant: charged particle precipitation onto sphere, 296 charging of lossy cylinder, 273 discharge of earth's atmosphere, 197 distributed lossy cable, 192-194 magnetic diff[r]
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## BÁO CÁO HÓA HỌC: " CONTROLLED GROWTH OF CARBON SPHERES THROUGH THE MG-REDUCTION ROUTE" PDF

hexachlorobutadiene is also encapsulated. In the new- formed carbon spheres, hexachlorobutadiene reacts with Mg continuously and produce MgCl 2 that can be washed out by water. While the Mg is consumed completely, the hollow carbon spheres were formed. Here, the partially consumed Mg powders acted as the template; therefore, the mediate Mg powders became smaller than their initial ones. The sizes of the hollow carbon particles may not be consistent with sizes of the initial Mg powders. At a higher reaction temperature (480 °C), the hollow capsules were prepared. This suggests that more energy is needed to form hollow capsules, which may be due to larger surface strain of capsules. If the temperature is increased up to 600 °C, the solid carbon spheres were produced. The formation of a solid carbon sphere may correlate with the nucleation of a carbon ring followed by a spiral shell growth, which has been proposed to explain the formation mechanism of solid carbon spheres [20]. More energy may be needed for the formation of the spiral shell growth than that of the carbon hollow capsules. So, the reaction temperature needs to be increased further for the formation of solid carbon spheres. The details of the process for the formation of carbon hollow spheres, hollow capsules and solid spheres are still not very clear. More in-depth studies are needed. The whole process can be schematically described as follows (as shown in Fig. 5).
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## A preliminary study on the current situation of the green areas and water bodies in the inner city of Hanoi

In Hanoi, the capital city of Vietnam, the awareness of the roles and benefits of greening in both previously and recently urbanised areas has been growing over the years. Green areas and water bodies play a vital role in maintaining the city as a comfortable living environment for residents and making it also a bio-sphere for numerous species as far as bio-diversity is concerned.
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## Numerical experiments using CHIEF to treat the nonuniqueness in solving acoustic axisymmetric exterior problems via boundary integral equations

The problem of nonuniqueness (NU) of the solution of exterior acoustic problems via boundary integral equations is discussed in this article. The efficient implementation of the CHIEF (Combined Helmholtz Integral Equations Formulation) method to axisymmetric problems is studied. Interior axial fields are used to indicate the solution error and to select proper CHIEF points. The procedure makes full use of LU-decomposition as well as the forward solution derived in the solution. Implementations of the procedure for hard spheres are presented. Accurate results are obtained up to a normalised radius of ka = 20.983, using only one CHIEF point. The radiation from a uniformly vibrating sphere is also considered. Accurate results for ka up to 16.927 are obtained using two CHIEF points.
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## DEVELOPMENT OF STUDENTS’ ENGLISH FOR SPECIAL PURPOSES COMPETENCE IN TOURISM STUDIES AT TERTIARY LEVEL POTX

Development of students’ English for Special Purposes competence in tourism studies at tertiary level . Dr. Ineta Luka, School of Business Administration Turiba, Latvia. empirical needs analysis conducted from September 2003 to September 2004. 137 respondents (99 tourism students, 12 tourism educators, and 26 tourism employers) took part in this stage of the research. First, narrative interviews with a group of 9 third-year tourism students were conducted. Their aim was to study the basic situations in which the students had used the English language at work, as well as to study the used language skills. Second, based on the gained results a standard questionnaire including the mentioned language themes was designed and a quantitative survey of 90 second- year tourism students applying it was conducted. Its aim was to get more detailed information about the use of the English language in tourism industry. Frequencies were analysed and Chi square value was determined. Next, 12 semi-structured interviews with tourism educators were conducted. Their aim was to gain information about the components of tourism specialist’s ESP competence and about the syllabus of an ESP course that would further the fulfilment of the curriculum requirements. Finally, in order to study the necessity of using English when being a lower level, medium level and top-level employee of a tourism establishment a quantitative survey of 26 tourism employers was conducted. Frequencies were analysed and Student’s T test value was determined.
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## SPHERE PACKINGS PPTX

Preface Sphere packings is one of the most fascinating and challenging subjects in mathematics. Almost four centuries ago, Kepler studied the densities of sphere packings and made his famous conjecture. Several decades later, Gregory and Newton discussed the kissing numbers of spheres and proposed the Gregory-Newton problem. Since then, these problems and related ones have attracted the attention of many prominent mathematicians such as Blichfeldt, Dirichlet, Gauss, Hermite, Korkin, Lagrange, Minkowski, Thue, Voronoi, Watson, and Zolotarev, as well as many active today. As work on the classical sphere packing problems has progressed many exciting re- sults have been obtained, ingenious methods have been created, related challenging problems have been proposed and investigated, and surprising connections with other subjects have been found. Thus, though some of its original problems are still open, sphere packings has developed into an important discipline.
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## MICROMECHANICAL PHOTONICS H UKITA PART 6 POT

Figure 3.18 shows the axial trapping eﬃciency dependence on the distance from the optical ﬁber end for a polystyrene sphere of radii 2.0 and 2 . 5 µ m. The laser beam proﬁle is Gaussian and the wavelength is 1 . 3 µ m. It is seen from the ﬁgure that trapping force increases as axial distance increases from zero to a beam waist of 40 µ m, i.e., it increases over the region in which the ﬁber lens is focusing, and then begins to decrease monotonically as the beam diverges beyond the focus. Therefore, we can expect that the optimum dual ﬁber lens spacingwill exists at a point where axial trappingeﬃciency is changing rapidly (see Sect. 3.3.4).
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## Handbook of mathematics for engineers and scienteists part 15 pot

3.3.2-1. Basic notions and properties. A figure formed by three great circle arcs pairwise connecting three arbitrary points on the sphere is called a spherical triangle (Fig. 3.37a). The vertices of a spherical triangle are the points of intersection of three rays issuing from the center of the sphere with the sphere. The angles less than π between the rays are called the sides a , b , and c of a spherical
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## APPLIED SURGICAL PHYSIOLOGY VIVAS PART 5 DOCX

in the alveolar pressure to above atmospheric. This leads to airflow out of the lungs 䊉 The point just before inspiration marks the eq uilibrium p o in t . The tendency of the lung to collapse due to its elastic recoil is prevented by the forces that hold the chest wall in position. The constant elastic recoil of the lung leads to a resting intrapleural pressure of 5 cmH 2 O below
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## Advances in Sonar Technology 2012 Part 7 doc

3.1.5 Local statistical description In the previous sections, a global statistical description of the SAS images has been given, ignoring the presence of any echoes. This is fair since the number of target pixels in the image is too small to significantly modify the global statistics. The observed histogram matches indeed very well a Weibull law. In this section, we study local first- and second-order statistical properties. This is achieved by looking at the data through a small sliding window composed of few pixels. In this case, the potential presence of echoes can no longer be ignored. Each echo is modeled as a deterministic element with an amplitude D surrounded by a noisy background with a Weibull distribution. We assume that the noise correlation is smaller than the spatial extension of the target echo and that the amplitude fluctuation of the echo is negligible. This is consistent with the experiments where the echoes appear as small sets of connected pixels with an almost constant value. This is justified in Fig. 8(b) with the pixels corresponding to echoes fitting the predicted ellipse in the mean–standard deviation plane.
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## LUYỆN THI THPT TEST 2 DOC

Choose the word which is stressed differently from the rest. 1. a. opponent b. countryman c. vertical d. aerial 2. a. camel b. panda c. extinct d. cactus 3. a. science b. reform c. standard d. measure 4. a. conduction b. consumer c. introduce d. position 5. a. available b. education c. particular d. certificate
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## THE GRAMMAR OF THE ENGLISH VERB PHRASE PART 116 PPTX

Perfect of experience (or experiential perfect ): (in this work), a particular usage type ( ⫽ a functional reading) of the indefinite perfect, namely one which refers to the actualization of one or more W-bygone situations which are not neces- sarily recent but which are ‘carried along’ as part of one’s experience and knowledge. For example: Have you ever been to Casablanca? .
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## SAT II MATH EPISODE 2 PART 4 POTX

17. The correct answer is (D). If in p – q > 0 we let q = 0, it follows that p – 0 > 0 or p > 0. 18. The correct answer is (E). From the information given, we can determine any of the angles at T. However, since we do not know SQ and cannot compute it, it follows that there is not enough information to compute PR .
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## Mobile Robots Perception & Navigation Part 2 potx

outdoors such as “Go down to the big tree and turn left.” Inherent in such a paradigm is the robot being able to recognize a “big tree” and do it in unstructured environments without too many pre-mapped fixed landmarks. Ultimately we envision mobile robots that unobtrusively mix in with pedestrian traffic and hence traveling primarily at a walking pace. With regard to sensors this is a different problem from robots designed to drive on roadways, since the necessary range of sensors is tied to the speed of the robot. It’s also important to note that small mobile robots that are intended to mix with pedestrian traffic must normally travel at the same speed as the pedestrians, even if they occasionally scurry quickly down a deserted alley or slow way down to traverse a tricky obstacle, because people resent having to go around a slow robot while they are also easily startled by machines such as Segways that overtake them without warning. At walking speeds the range of sonar at about 50kHz is optimal, and there are none of the safety concerns one might have with lidar, for example. This type of sonar is precisely what bats use for echolocation; the goal of our research is to employ sonar sensors to allow mobile robots to recognize objects in the everyday environment based on simple signal processing algorithms tied to the physics of how the sonar backscatters from various objects. Our primary interest is for those sensors that can function well outdoors without regard to lighting conditions or even in the absence of daylight. We have built several 3D sonar scanning systems packaged as sensor heads on mobile robots, so that we are able to traverse the local environment and easily acquire 3D sonar scans of typical objects and structures. Of course sonar of the type we’re exploring is not new. As early as 1773 it was observed that bats could fly freely in a dark room and pointed out that hearing was an important component of bats’ orientation and obstacle avoidance capabilities (Au, 1993). By 1912 it was suggested that bats use sounds inaudible to humans to detect objects (Maxim, 1912) but it wasn’t until 1938 that Griffin proved that bats use ultrasound to detect objects (Griffin, 1958).
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## ENGLISH TEST 5 PDF

ENGLISH TEST 5 Choose the word which is stressed differently from the rest. 1. a. opponent b. countryman c. vertical d. aerial 2. a. camel b. panda c. extinct d. cactus 3. a. science b. reform c. standard d. measure 4. a. conduction b. consumer c. introduce d. position 5. a. available b. education c. particular d. certificate
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## COMPUTATIONAL TECHNIQUES FOR SIMULATING THE INTERACTIONS BETWEEN PEPTIDES AND CARBON NANOTUBES

and insights into the nature of free energy landscapes can be obtained. Therefore the model has been successfully applied to explore kinetics and thermodynamics of protein folding in bulk solvent and adsorption onto various surfaces. In this chapter, I extend the previous work to study the mechanism of peptides interacting with CNTs using HP lattice model and MC simulation method. In Section 4.1, the simulation models and methods are presented. Exact enumeration of all the possible conformations of peptides has been carried out on 2D lattices with the chain length of 16 residues. In order to simulate the peptide-CNT interactions, a model wall with an energetically favorable potential to peptide beads is introduced. In Section 4.2, thermodynamics and conformational changes of peptides folding in bulk water and interacting with CNTs are discussed. The hydrophobicity of the CNT is incorporated into the existing HP lattice paradigm and the interaction parameters between model chain residues and the CNT monomers can be qualitatively determined based on experimental data and simulation results from the all-atom model. Section 4.3 discusses the comparison between MD and MC algorithms, and Section 4.4 gives the remarks of the chapter.
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## BIODEGRADABLE DENDRIMERS AND DENDRITIC POLYMERS

10.4 Biological Implications of Biodegradable Dendrimers 257 in the form of highly branched dendritic architectures [52] . The interesting applica- tion of these intriguing and well - deﬁ ned materials seems to be branching out. Especially, they offer water solubility due to enriched hydrophilic groups at the surface, ester linkages to make them biodegradable, and appropriate amounts of drug can be added so that a uniform supply of the drug is delivered when the polymer degrades. Dendrimers ﬁ nd implications in biology for delivering drugs, bioactives (e.g., SiRNA and peptides), diagnostics (dyes), and in targeted delivery systems (use of LHRH peptide, folic acid, antibodies, etc.) [14, 21, 22, 37, 43, 44] . Among many other crucial characteristics of cellular internalization of dendritic architectures, the ability of dendrimers to cross cell membrane is of much interest particularly for their application in drug and gene delivery. A recent study has demonstrated that dendrimers are capable to enter cells by endocytosis, but the intracellular pathway following their internalization remains controversial [53] . The intracellular trafﬁ cking property of PAMAM dendrimers was observed using confocal ﬂ uorescence microscopy with high spatial and temporal resolution in living HeLa cells. Macromolecules of different chemical functionality (neutral, cationic, and lipidated), size (from G2 up to G6), and surface charge are investi- gated and their internalization properties correlated with the molecular structure. So far, not many strategies have been reported to synthesize biodegradable den- drimers and among them very few suggest their biomedical applications. Section 10.5 highlights biological perspectives of biodegradable dendrimers.
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## Tài Liệu Ôn Thi Vào Trần Đại Nghĩa

Graph: biểu đồ Combine: kết hợp Expression= statement phát biểu, biểu thức Total : tổng số Solid: khối hình Figure: hình dáng Cube: hình lập phương Cone: hình nón. Sphere: hình c[r]
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## Tài liệu DEVELOPMENT OF INCOME SECURITY docx

envelops” by the Vietnamese. Even support in family alone, support from “economy of envelop” far exceed support of social security system 19 . Vietnamese culture in influenced by Buddhism and Confucianism which encourage offspring to finance and take care of their parents after having grown up. The financial support can be regular or on the certain occasions as Tet (Lunar New Year). The amount of financial support expresses the status and financial ability of the offspring. The traditional financial support still remains after Doi Moi (innovation) and even is developed due to high economic growth. Besides direct responsibility to parents, Vietnamese people also have limited responsibility to siblings and wife’s or husband’s family (aunts and uncles). Unofficial financial support such as city-dwellers sends money to close relatives in the countryside. Another mutual support is financial support through weddings, funerals. However the support in the urban and rural areas has great differences. Families in cities only focus on receiving envelopes of money while families in the countryside have to save a great amount of incomes/ agricultural products for the events (weddings, funerals, and worshipping days) especially in 3 months at the end of the year. Farmers have to spend 20% of family income on the events above in months late in a year. The money they receive will be spent on repaying in similar events by the host. In addition, when they buy land and build a house, they mainly borrow money with zero interest from unofficial sources such as close relatives, friends instead of from banks. “Money deposit” is a means of transferring money to support each other among close relatives and is thus practiced between relatives living far from each other. Form and scale of the deposit, therefore, are affected by migration. “Money deposit” of emigrants especially from the rural to the urban areas is an important source to supplement income and reduce poverty. “Money deposit” accounts for 60-70% of income in cash of families in the countryside. According to the recent survey of General Department of Statistics and the United Nations Population Fund (2004), 60% of men and 57% of women who migrate to big Ha Noi, Ho Chi Minh City, Economic Zone in Northeast Vietnam, High Land of the Central Vietnam, Industrial Park in Southeast Vietnam have sent VND 1-6 millions (62, 5 – 375 thousand dollars) back to their families in the countryside in 12 months before the survey carried out.
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## ESSENTIAL ELECTROMAGNETISM: SOLUTIONS - EBOOKS AND TEXTBOOKS FROM BOOKBOON

a Find the surface magnetisation current density, and use this to ﬁnd the magnetic M0 � dipole moment of the sphere.. Compare this with what you expect given the volume of the sphere and[r]
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## ESSENTIAL ELECTROMAGNETISM: SOLUTIONS - EBOOKS AND TEXTBOOKS FROM BOOKBOON

a Find the surface magnetisation current density, and use this to ﬁnd the magnetic M0 � dipole moment of the sphere.. Compare this with what you expect given the volume of the sphere and[r]
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## HEAT TRANSFER HANDBOOK PART 20 PDF

with air, and the heat transfer at the interface is the sum of solid conduction across the contact points and ﬂuid conduction through the gaps. Because ofthe imperfect contact, there is a temperature drop across the gap or interface, ∆ T c . The contact conductance h c (W/m 2 · K) is deﬁned as the ratio ofthe heat ﬂux q/A through the interface to the interface temperature drop:
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## BÁO CÁO TOÁN HỌC: "A UNIFORM APPROACH TO COMPLEXES ARISING FROM FORESTS" PPS

In the recent years several complexes arising from forests have been studied by different authors with different techniques (see [EH], [E], [K1], [K2], [MT], [W]). The interest in these problems is motivated by applications in different contexts, such as graph theory and statistical mechanics ([BK], [BLN], [J]). We introduce a unifying approach to study the homotopy type of many of these complexes. With our technique we obtain simple proofs of results that were already known as well as new results. These complexes are ho- motopic to wedges of spheres of (possibly) different dimensions and include, for instance, the complexes of directed trees, the independence complexes, the dominance complexes, the matching complexes, the interval order complexes. In all cases our method provides a recursive procedure to compute the exact homotopy type of the simplicial complex. The dimensions of the spheres arising with these constructions are often strictly related to well-known graph theoretical invariants of the underlying forest such as the domina- tion number, the independent domination number, the vertex covering number and the matching number. Thus we give a topological interpretation to these classical combina- torial invariants.
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## ĐỀ TÀI " NEW UPPER BOUNDS ON SPHERE PACKINGS I " DOCX

7. Numerical results It is possible to get numerical results by using linear programming to ﬁnd functions for use in Theorem 3.1, as was done for the kissing problem by Odlyzko and Sloane in [OS]. The idea is to ﬁx one of f (0) and f (0), and view extremizing the other as an inﬁnite-dimensional linear programming problem. One can try to approximate it with a ﬁnite-dimensional problem, and solve it on a computer. Although we obtained some numerical results this way, it was cumbersome and generally ineﬀective. Instead, we use the following approach. First, consider trying to use our techniques to bound the density of an isodual lattice. There is no reason for optimal sphere packings to be isodual lattices, and for example in three dimensions they are known not to be, but it is convenient to use this case as a stepping stone.
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## Plasmonic thin film InP/graphene-based Schottky-junction solar cell using nanorods

Herein, the design and simulation of graphene/InP thin film solar cells with a novel periodic array of nanorods and plasmonic back-reflectors of the nano-semi sphere was proposed. In this structure, a single-layer of the graphene sheet was placed on the vertical nanorods of InP to form a Schottky junction. The electromagnetic field was determined using solving three-dimensional Maxwell’s equations discretized by the finite difference method (FDM). The enhancement of light trapping in the absorbing layer was illustrated, thereby increasing the short circuit current to a maximum value of 31.57 mA/cm2 with nanorods having a radius of 400 nm, height of 1250 nm, and nano-semi sphere radius of 50 nm, under a solar irradiation of AM1.5G. The maximum ultimate efficiency was determined to be 45.8% for an angle of incidence of 60 . This structure has shown a very good light trapping ability when graphene and ITO layers were used at the top and as a back-reflector in the proposed photonic crystal structure of the InP nanorods. Thence, this structure improves the short-circuit current density and the ultimate efficiency of 12% and 2.7%, respectively, in comparison with the InP-nanowire solar cells.
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