Maximal sets of Hamilton cycles in Kn,n

In this article, we prove that there exists a maximal set of m Hamilton cycles in K-n,K-n if and only if n/4 < m less than or equal to n/2. (C) 2000 John Wiley & Sons, Inc.

Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

Hamilton decompositions of 6-regular abelian Cayley graphs

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made: Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian. The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture: Alspach Conjecture: Every 2k-regular, connected Cayley graph on a finite abelian group has a Hamilton decomposition. Alspach’s conjecture is true for k = 1 and 2, but even the case k = 3 is still open. It is this case that this thesis addresses. Chapters 1–3 give introductory material and past work on the conjecture. Chapter 3 investigates the relationship between 6-regular Cayley graphs and associated quotient graphs. A proof of Alspach’s conjecture is given for the odd order case when k = 3. Chapter 4 provides a proof of the conjecture for even order graphs with 3-element connection sets that have an element generating a subgroup of index 2, and having a linear dependency among the other generators. Chapter 5 shows that if Γ = Cay(A, {s1, s2, s3}) is a connected, 6-regular, abelian Cayley graph of even order, and for some1 ≤ i ≤ 3, Δi = Cay(A/(si), {sj1 , sj2}) is 4-regular, and Δi ≄ Cay(ℤ3, {1, 1}), then Γ has a Hamilton decomposition. Alternatively stated, if Γ = Cay(A, S) is a connected, 6-regular, abelian Cayley graph of even order, then Γ has a Hamilton decomposition if S has no involutions, and for some s ∈ S, Cay(A/(s), S) is 4-regular, and of order at least 4. Finally, the Appendices give computational data resulting from C and MAGMA programs used to generate Hamilton decompositions of certain non-isomorphic Cayley graphs on low order abelian groups.

On the Hamilton-Waterloo problem

The Hamilton-Waterloo problem asks for a 2-factorisation of K-v in which r of the 2-factors consist of cycles of lengths a(1), a(2),..., a(1) and the remaining s 2-factors consist of cycles of lengths b(1), b(2),..., b(u) (where necessarily Sigma(i)(=1)(t) a(i) = Sigma(j)(=1)(u) b(j) = v). In thus paper we consider the Hamilton-Waterloo problem in the case a(i) = m, 1 less than or equal to i less than or equal to t and b(j) = n, 1 less than or equal to j less than or equal to u. We obtain some general constructions, and apply these to obtain results for (m, n) is an element of {(4, 6)1(4, 8), (4, 16), (8, 16), (3, 5), (3, 15), (5, 15)}.

Hamilton-Waterloo problem with triangle and C9 factors

The Hamilton-Waterloo problem and its spouse-avoiding variant for uniform cycle sizes asks if Kv, where v is odd (or Kv - F, if v is even), can be decomposed into 2-factors in which each factor is made either entirely of m-cycles or entirely of n-cycles. This thesis examines the case in which r of the factors are made up of cycles of length 3 and s of the factors are made up of cycles of length 9, for any r and s. We also discuss a constructive solution to the general (m,n) case which fixes r and s.

Effect Of Simulated Microwave Disinfection On The Linear Dimensional Change, Hardness And Impact Strength Of Acrylic Resins Processed By Different Polymerizing Cycles.

This study investigated the effect of simulated microwave disinfection (SMD) on the linear dimensional changes, hardness and impact strength of acrylic resins under different polymerization cycles. Metal dies with referential points were embedded in flasks with dental stone. Samples of Classico and Vipi acrylic resins were made following the manufacturers' recommendations. The assessed polymerization cycles were: A-- water bath at 74ºC for 9 h; B-- water bath at 74ºC for 8 h and temperature increased to 100ºC for 1 h; C-- water bath at 74ºC for 2 h and temperature increased to 100ºC for 1 h;; and D-- water bath at 120ºC and pressure of 60 pounds. Linear dimensional distances in length and width were measured after SMD and water storage at 37ºC for 7 and 30 days using an optical microscope. SMD was carried out with the samples immersed in 150 mL of water in an oven (650 W for 3 min). A load of 25 gf for 10 sec was used in the hardness test. Charpy impact test was performed with 40 kpcm. Data were submitted to ANOVA and Tukey's test (5%). The Classico resin was dimensionally steady in length in the A and D cycles for all periods, while the Vipi resin was steady in the A, B and C cycles for all periods. The Classico resin was dimensionally steady in width in the C and D cycles for all periods, and the Vipi resin was steady in all cycles and periods. The hardness values for Classico resin were steady in all cycles and periods, while the Vipi resin was steady only in the C cycle for all periods. Impact strength values for Classico resin were steady in the A, C and D cycles for all periods, while Vipi resin was steady in all cycles and periods. SMD promoted different effects on the linear dimensional changes, hardness and impact strength of acrylic resins submitted to different polymerization cycles when after SMD and water storage were considered.

Effect Of Simulated Microwave Disinfection On The Linear Dimensional Change, Hardness And Impact Strength Of Acrylic Resins Processed By Different Polymerization Cycles.

This study investigated the effect of simulated microwave disinfection (SMD) on the linear dimensional changes, hardness and impact strength of acrylic resins under different polymerization cycles. Metal dies with referential points were embedded in flasks with dental stone. Samples of Classico and Vipi acrylic resins were made following the manufacturers' recommendations. The assessed polymerization cycles were: A) water bath at 74 ºC for 9 h; B) water bath at 74 ºC for 8 h and temperature increased to 100 ºC for 1 h; C) water bath at 74 ºC for 2 h and temperature increased to 100 ºC for 1 h; and D) water bath at 120 ºC and pressure of 60 pounds. Linear dimensional distances in length and width were measured after SMD and water storage at 37 ºC for 7 and 30 days using an optical microscope. SMD was carried out with the samples immersed in 150 mL of water in an oven (650 W for 3 min). A load of 25 gf for 10 s was used in the hardness test. Charpy impact test was performed with 40 kpcm. Data were submitted to ANOVA and Tukey's test (5%). The Classico resin was dimensionally steady in length in the A and D cycles for all periods, while the Vipi resin was steady in the A, B and C cycles for all periods. The Classico resin was dimensionally steady in width in the C and D cycles for all periods, and the Vipi resin was steady in all cycles and periods. The hardness values for Classico resin were steady in all cycles and periods, while the Vipi resin was steady only in the C cycle for all periods. Impact strength values for Classico resin were steady in the A, C and D cycles for all periods, while Vipi resin was steady in all cycles and periods. SMD promoted different effects on the linear dimensional changes, hardness and impact strength of acrylic resins submitted to different polymerization cycles when after SMD and water storage were considered.

Effect Of Sodium Hypochlorite And Peracetic Acid On The Surface Roughness Of Acrylic Resin Polymerized By Heated Water For Short And Long Cycles.

To evaluate the surface roughness of acrylic resin submitted to chemical disinfection via 1% sodium hypochlorite (NaClO) or 1% peracetic acid (C2H4O3). The disc-shaped resin specimens (30 mm diameter ×4 mm height) were polymerized by heated water using two cycles (short cycle: 1 h at 74°C and 30 min at 100°C; conventional long cycle: 9 h at 74°C). The release of substances by these specimens in water solution was also quantified. Specimens were fabricated, divided into four groups (n = 10) depending on the polymerization time and disinfectant. After polishing, the specimens were stored in distilled deionized water. Specimens were immersed in 1% NaClO or 1% C2H4O3 for 30 min, and then were immersed in distilled deionized water for 20 min. The release of C2H4O3 and NaClO was measured via visual colorimetric analysis. Roughness was measured before and after disinfection. Roughness data were subjected to two-way ANOVA and Tukey's test. There was no interaction between polymerization time and disinfectant in influencing the average surface roughness (Ra, P = 0.957). Considering these factors independently, there were significant differences between short and conventional long cycles (P = 0.012), but no significant difference between the disinfectants hypochlorite and C2H4O3 (P = 0.366). Visual colorimetric analysis did not detect release of substances. It was concluded that there was the difference in surface roughness between short and conventional long cycles, and disinfection at acrylic resins polymerized by heated water using a short cycle modified the properties of roughness.

Isotopic view of vegetation and carbon and nitrogen cycles in a cerrado ecosystem, southeastern Brazil

Carbon and nitrogen biogeochemical cycles in savannas are strongly regulated by the seasonal distribution of precipitation and pulses of nutrients released during the wetting of the dry soil and are critical to the dynamics of microorganisms and vegetation. The objective of this study was to investigate the spatial and temporal variability of C and N isotope ratios as indicators of the cycling of these elements in a cerrado sensu stricto area, within a protected area in a State Park in the state of São Paulo, Brazil. The foliar δ13C and δ15N values varied from -33.6 to -24.4 ‰ and -2.5 to 4.5 ‰, respectively. The δ13C values showed a consistent relationship with canopy height, revealing the importance of structure of the canopy over the C isotopic signature of the vegetation. Carbon isotopic variations associated with the length of the dry season indicated the importance of recent fixed C to the integrated isotopic signature of the leaf organic C. The studied Cerrado species showed a depleted foliar δ15N, but a wide range of foliar Nitrogen with no difference among canopy heights. However, seasonal variability was observed, with foliar δ15N values being higher in the transition period between dry and rainy seasons. The variation of the foliar C and N isotope ratios presented here was consistent with highly diverse vegetation with high energy available but low availability of water and N.

Modeling Two-Oscillator Circadian Systems Entrained by Two Environmental Cycles

Several experimental studies have altered the phase relationship between photic and non-photic environmental, 24 h cycles (zeitgebers) in order to assess their role in the synchronization of circadian rhythms. To assist in the interpretation of the complex activity patterns that emerge from these ""conflicting zeitgeber'' protocols, we present computer simulations of coupled circadian oscillators forced by two independent zeitgebers. This circadian system configuration was first employed by Pittendrigh and Bruce (1959), to model their studies of the light and temperature entrainment of the eclosion oscillator in Drosophila. Whereas most of the recent experiments have restricted conflicting zeitgeber experiments to two experimental conditions, by comparing circadian oscillator phases under two distinct phase relationships between zeitgebers (usually 0 and 12 h), Pittendrigh and Bruce compared eclosion phase under 12 distinct phase relationships, spanning the 24 h interval. Our simulations using non-linear differential equations replicated complex non-linear phenomena, such as ""phase jumps'' and sudden switches in zeitgeber preferences, which had previously been difficult to interpret. Our simulations reveal that these phenomena generally arise when inter-oscillator coupling is high in relation to the zeitgeber strength. Manipulations in the structural symmetry of the model indicated that these results can be expected to apply to a wide range of system configurations. Finally, our studies recommend the use of the complete protocol employed by Pittendrigh and Bruce, because different system configurations can generate similar results when a ""conflicting zeitgeber experiment'' incorporates only two phase relationships between zeitgebers.

Role of noise in population dynamics cycles

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.

Cryptic species, life cycles, and the phylogeny of Clytia (Cnidaria: Hydrozoa: Campanulariidae)

Medusae and polyps of Clytia are abundantly found in coastal marine environments and one species in the genus-Clytia hemisphaerica (Linnaeus, 1767)-has become an important experimental model. Yet, only 10 species in the genus have had their life cycle investigated. Most species of Clytia are also poorly described, and detailed life cycle and morphological studies are needed for accurate species-level identifications. Here, we investigated the life cycle of Clytia elsaeoswaldae Stechow, 1914, a species described for the tropical western Atlantic and subsequently considered conspecific to the nearly-cosmopolitan species Clytia gracilis (Sars, 1850) and Clytia hemisphaerica, originally described for the temperate North Atlantic. Based on observations of mature medusae and multiple colonies from southeastern Brazil and the U. S. Virgin Islands (type locality), our results show that C. elsaeoswaldae is morphologically distinct from C. gracilis and C. hemisphaerica. The morphological results are corroborated by a multigene phylogenetic analysis of the genus Clytia, which shows that C. gracilis-like species form a polyphyletic group of several species. These results suggest that the nearly-cosmopolitan distribution attributed to some species of Clytia may be due to the non-recognition of morphologically similar species with more restricted ranges.

Electrochemical impedance spectroscopy investigation of the electrochemical behaviour of copper coated with artificial patina layers and submitted to wet and dry cycles

Due to rain events historical monuments exposed to the atmosphere are frequently submitted to wet and dry cycles. During drying periods wetness is maintained in some confined regions and the corrosion product layer, generally denominated patinas, builds up and gets thicker. The aim of this study is to use electrochemical impedance spectroscopy (EIS) to investigate the electrochemical behaviour of pure copper coated with two artificial patina layers and submitted either to continuous or to intermittent immersion tests, this latter aiming to simulate wet and dry cycles. The experiments were performed in 0.1 mol dm(-3) NaCl solution and in artificial rainwater containing the most significant pollutants of the city of Sao Paulo. The results of the continuous immersion tests in the NaCl solution have shown that the coated samples behave like a porous electrode with finite pore length. On the other hand, in the intermittent tests a porous electrode response with semi-infinite pore length can be developed. The results were interpreted based on the model of de Levie and a critical comparison with previous interpretations reported in the literature for similar systems is presented. (C) 2011 Elsevier Ltd. All rights reserved.

Supercritical steam cycles and biomass integrated gasification combined cycles for sugarcane mills

Back in 1970s and 1980s, cogeneration plants in sugarcane mills were primarily designed to consume all bagasse, and produce steam and electricity to the process. The plants used medium pressure steam boilers (21 bar and 300 degrees C) and backpressure steam turbines. Some plants needed also an additional fuel, as the boilers were very inefficient. In those times, sugarcane bagasse did not have an economic value, and it was considered a problem by most mills. During the 1990s and the beginning of the 2000s, sugarcane industry faced an open market perspective, thus, there was a great necessity to reduce costs in the production processes. In addition, the economic value of by-products (bagasse, molasses, etc.) increased, and there was a possibility of selling electricity to the grid. This new scenario led to a search for more advanced cogeneration systems, based mainly on higher steam parameters (40-80 bar and 400-500 degrees C). In the future, some authors suggest that biomass integrated gasification combined cycles are the best alternative to cogeneration plants in sugarcane mills. These systems might attain 35-40% efficiency for the power conversion. However, supercritical steam cycles might also attain these efficiency values, what makes them an alternative to gasification-based systems. This paper presents a comparative thermoeconomic study of these systems for sugarcane mills. The configurations studied are based on real systems that could be adapted to biomass use. Different steam consumptions in the process are considered, in order to better integrate these configurations in the mill. (C) 2009 Elsevier Ltd. All rights reserved.