... k A card of weight k is a connected k-graph labelled by any k natural numbers Equivalently, a card can be specified as a picture and a set of natural number labels To construct the card we label ... between the cardinality ofthe sets of hands and the cardinality ofthe decks For example, when dealing with labelled graphs, Dk is the set of all connected k-graphs whose vertices are labelled by ... refer to as pictures of weight k A card of weight k is a pair consisting ofa picture of weight k and a k-element subset of N that we will call the label set ofthe card A hand of weight n and size...
... 0, j Thenumberof matchings ina tree In this section, we turn to thenumberof matchings ina graph This is also known as the Hosoya index, or the Z-index in mathematical chemistry For a rooted ... An interesting paper of Wagner [5] looks at thenumberof independent sets modulo m Wagner showed that the proportion of trees on n vertices with thenumberof independent sets ... set as a matching as well Applying the previous technique, we will show the following the electronic journal of combinatorics 17 (2010), #N18 Theorem For m ∈ N, B(m) = Z2 m There are formulae...
... details on the Tiameslan line can be found in Zhang et al [25] All animals were weighed at weaning and at the beginning ofthe test period (at and weeks of age, respectively) At the end ofthe ... variance and the remaining part was assigned to error variance The same starting values were used inthe three chains for the other parameters, i.e zero for polygenic and major gene additive and ... for ABT, X2 and X4 For X5, only 4% ofthe breeding animals had a favourable genotype All breeding animals had at least one copy ofthe dominant alleles decreasing NTY and FTN and increasing GTN...
... models, assisted in data collection, analyzed the data, and drafted the manuscript CP and EM assisted with data analysis and drafting ofthe manuscript All authors read and approved the final manuscript ... regulate the material taught inthe classroom and set exact goals for thenumberof procedures that must be completed during practical training, and the new national training quality standards mandate ... Government of Zambia Ministry of Health: Ministry of Health Annual Training and Development Plan 2008 Lusaka, Zambia 2008 13 Government of Zambia Ministry of Health: Educational Infrastructure and Teaching...
... Ideal shapes of (a) the discriminant functions and (b) the associated cost function, for N = estimate, the eigenvalue variation can be still used, ina different form, for obtaining N The main ... their difference allows quite satisfactorily the estimation of N PARTICULAR CASE OFA LINEAR PIECEWISE VARIATION OFTHE AUTOCORRELATION MATRIX EIGENVALUES The theoretical validity of this criterion ... 0.9 Finally, the third type of simulations have been devoted to a high-resolution radar application The goal is to find the most accurate estimate oftherange profile ofa radar target using its...
... apply the induction hypothesis using the paths P and Q to obtain a path R satisfying the lemma Next, we repeat the above argument with the portion of R beginning at um−1 and the vertex um Theorem ... there is a unique hamiltonian path of T that avoids this arc Hence, there are 2n−2 + distinct hamiltonian paths ina nearly transitive tournament of order n Lemma Let T be a strong tournament of order ... be x0 Then C and V \ {x1 , x2 } satisfy the lemma Next, assume that T contains a vertex v such that T − v is not strong and that no sets A and B satisfy the lemma Let t be thenumberof strong...
... Jnq,d is the all one matrix and Inq,d is the identity matrix, both of size nq,d × nq,d ) Therefore, the largest eigenvalue of V is Dq,d and the absolute valuesof all other eigenvalues are either ... completing the proof of Theorem 1.2 Acknowledgments The research is performed during the author’s visit at the Erwin Schr¨dinger International o Institute for Mathematical Physics The author ... works intherange d > k (as larger tuples of mutually orthogonal vectors are out ofrangeofthe methods uses) while Theorem 1.2 works ina wider range d > 2(k − 1) Moreover, Theorem 1.2 is stronger...
... regarding thenumberof independent sets in trees Another graph parameter popular in statistical physics and in mathematical chemistry is the Hosoya index which is thenumberof matchings inthe ... argue that thenumberof F -matchings in each such class is a zero residue Indeed, thenumberof F -matchings ina given class Ci is precisely thenumberof F -matchings inthe forest remaining from ... above In fact, the proof also works in other scenarios If a probability space of graphs has a property corresponding to the probabilistic part ofthe proof, then thenumberof (induced) F -matchings...
... reversing the numbering ofthe vertices, by which inward patterns become outward patterns and vice versa Note that thenumberof outward patterns and thenumberof inward patterns can readily ... (since they can not have an outgoing diagonal) Since the edges which are diagonals constitute a matching in G there are n diagonals Thus there are n 2 active vertices in total We now describe the ... have more than one option to decide which ofthe outgoing edges of vi to include Remark 2.2 v1 and v2 are active (since they can not have an incoming diagonal) whereas vn−1 and are passive (since...
... expands, the correct denotational relationship is maintained by expanding the image inthe table using the ~-expression, and then finding the corresponding element inthe model If the element inthe ... to a model has been augmented with a table that contains each ~-expression and the ima6e of its denotation inthe current stage ofthe dynamic model When the domain ofthe ~-expression expands, ... that was the denotation ofthe h-expression was not expanded inthe same way as the image in this table, a new element corresponding to the expanded image is added to the model This table allows...
... to interpreting the laws of apartheid illuminated debates in philosophy of law about the relationship between law and morality My main focus was on the statutory regime put in place to maintain ... ofin accordance with the rigid doctrine ofthe separation of powers; and, finally, functionalism, a theory ofthe administrative state that seeks to tame the judiciary in order to facilitate the ... that Smuts was a racist, whose own policies in South Africa laid the basis for apartheid: after all, in holding racist views, he was inthe mainstream of politics Rather, he strongly favoured a...
... to interpreting the laws of apartheid illuminated debates in philosophy of law about the relationship between law and morality My main focus was on the statutory regime put in place to maintain ... ofin accordance with the rigid doctrine ofthe separation of powers; and, finally, functionalism, a theory ofthe administrative state that seeks to tame the judiciary in order to facilitate the ... that Smuts was a racist, whose own policies in South Africa laid the basis for apartheid: after all, in holding racist views, he was inthe mainstream of politics Rather, he strongly favoured a...
... meet the needs ofthe members and the facilitators is the initial planning, organization, and setting up ofthe group This initial stage can easily be bypassed inthe interests of time and the ... logical relationship, and the feelings may come all at once in an inexplicable ball of raw emotion You may hear complaints of fatigue, exhaustion, lack of energy, pain, or inability to sleep All of ... Grief and the Sacred Art of Ritual Janet Shaw Rogers 129 Section III Alternative Art Forms, Programs, and Stories of Art and Healing Chapter 14 The Painters Deborah Koff-Chapin, Carol McIntyre, and...
... recombination awaits further investigation Conclusion The data presented in this paper show that the recTULV presents no real match to the original cell adapted variant and that the lower fitness ofthe ... draft the manuscript AlexP participated inthe design ofthe study and drafted the manuscript Both authors read and approved the final manuscript Acknowledgements 18 19 The authors thank Prof ... recTULV The purified and pre-passaged recombinant virus, however, presented no real match to the original cell adapted variant, TUL02, it terms of fitness Taking into account that thein situ...
... recombination awaits further investigation Conclusion The data presented in this paper show that the recTULV presents no real match to the original cell adapted variant and that the lower fitness ofthe ... draft the manuscript AlexP participated inthe design ofthe study and drafted the manuscript Both authors read and approved the final manuscript Acknowledgements 18 19 The authors thank Prof ... recTULV The purified and pre-passaged recombinant virus, however, presented no real match to the original cell adapted variant, TUL02, it terms of fitness Taking into account that thein situ...
... South Africa, there is an ongoing debate about whether or not the side-effect profile of HAART may adversely affect the HRQoL of HIVpositive individuals More data about the impact of HAART and HAARTrelated ... onto HAART and increasing survival among these patients, there is a growing need to understand the impact of HAART use on the quality of lives of HIVinfected individuals [4-8] There is a sizeable ... antiretroviral (ARV) therapy progressed to AIDS and died of their disease The rollout of highly active antiretroviral therapy (HAART) through national and provincial programmes has dramatically altered...
... to calculate the most likely ofthe four rot risk classes as a function, for each fixed basal area, ofthe age and the dominant height ofthe stand, obtaining for each value of basal area a graphic ... distribution ofthe age ofthe dominant strata and the site index within the forest area can be seen in Figure The classification ofthe forest area infunctionofthe stand age and the site index is ... numberof pairs of samples ua and ua + d which distance from each other is within the distance lag centred at d, and z(ua ) and z(ua +d) are thevalues that the variable z takes at samplesua and ua...
... ofthe challenge for the Treasury and the Fed, meanwhile, was to talk scores ofthe world's largest banks into not calling in their Korea loans All these initiatives came to a head at the same ... reserves of dollars This sequence of events led to the so-called Asian contagion, a series of financial crises that began with the collapse ofthe Thai baht and Malaysian ringgit inthe summer of 1997 ... it off was the initial public offering of Netscape, a tiny two-year-old software maker in Silicon Valley that had al- most no revenues and not a penny of profits Netscape was actually giving...
... history and the culture it has spawned By culture, I mean the shared valuesof members ofa society that are inculcated at an early age and that pervade all aspects of living Some aspects ofa nation's ... heavily invested in loans backed by real estate as collateral, as real estate prices soared When the turn came and prices cascaded downward, the collateral became inadequate But instead of calling ... which are already prominent in this book Australia and New Zealand are particularly interesting in how they developed after adopting market-opening reforms and gradually increasing ties with Asia,...