Oscilador harmônico unidimensional via transformada unilateral de Fourier e mapeamento do potencial de morse unidimensional nos potenciais pseudo-harmônico e de kratzer tridimensionais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Three-Dimensional Finite Element Analysis of Stress Distribution on Different Bony Ridges With Different Lengths of Morse Taper Implants and Prosthesis Dimensions

This finite element analysis (FEA) compared stress distribution on different bony ridges rehabilitated with different lengths of morse taper implants, varying dimensions of metal-ceramic crowns to maintain the occlusal alignment. Three-dimensional FE models were designed representing a posterior left side segment of the mandible: group control, 3 implants of 11 mm length; group 1, implants of 13 mm, 11 mm and 5 mm length; group 2, 1 implant of 11 mm and 2 implants of 5 mm length; and group 3, 3 implants of 5 mm length. The abutments heights were 3.5 mm for 13- and 11-mm implants (regular), and 0.8 mm for 5-mm implants (short). Evaluation was performed on Ansys software, oblique loads of 365N for molars and 200N for premolars. There was 50% higher stress on cortical bone for the short implants than regular implants. There was 80% higher stress on trabecular bone for the short implants than regular implants. There was higher stress concentration on the bone region of the short implants neck. However, these implants were capable of dissipating the stress to the bones, given the applied loads, but achieving near the threshold between elastic and plastic deformation to the trabecular bone. Distal implants and/or with biggest occlusal table generated greatest stress regions on the surrounding bone. It was concluded that patients requiring short implants associated with increased proportions implant prostheses need careful evaluation and occlusal adjustment, as a possible overload in these short implants, and even in regular ones, can generate stress beyond the physiological threshold of the surrounding bone, compromising the whole system.

Regularity at infinity of real mappings and a Morse-Sard theorem

We prove a new Morse-Sard-type theorem for the asymptotic critical values of semi-algebraic mappings and a new fibration theorem at infinity for C-2 mappings. We show the equivalence of three different types of regularity conditions which have been used in the literature in order to control the asymptotic behaviour of mappings. The central role of our picture is played by the p-regularity and its bridge toward the rho-regularity which implies topological triviality at infinity.

Alternativa protética para correção da angulação com componentes não indexados sobre implantes Cone Morse indexados: sistema tubo parafuso

From a recent perspective the morse-taper dental implants connections are increasingly being used as an alternative for replacement of a missing teeth. Nevertheless, there are a large variety of prosthetic components available on the market with some limitations regarding the final prothesis. This article demonstrated the difficulties and limitations of prosthesis implant-retained connections when using morse-taper implants (with a prosthetic index) case in which the surgical placement of the implant wasn’t successfully performed. The alternative to overcome this scenario was the technique using the tube screw over the top of a mini abutment component. It was possible to manufacture and to have satisfactory adaptation, achieving the satisfaction of the patient, restoring function and esthetics.

Morse taper implants at different bone levels: a finite element analysis of stress distribution

AIM: To explore the biomechanical effects of the different implantation bone levels of Morse taper implants, employing a finite element analysis (FEA). METHODS: Dental implants (TitamaxCM) with 4x13 mm and 4x11 mm, and their respective abutments with 3.5 mm height, simulating a screwed premolar metal-ceramic crown, had their design performed using the software AnsysWorkbench 10.0. They were positioned in bone blocks, covered by 2.5 mm thickness of mucosa. The cortical bone was designed with 1.5 mm thickness and the trabecular bone completed the bone block. Four groups were formed: group 11CBL (11 mm implant length on cortical bone level), group 11TBL (11 mm implant length on trabecular bone level), group 13CBL (13mm implant length on cortical bone level) and group 13TBL (13 mm implant length on trabecular bone level). Oblique 200 N loads were applied. Von Mises equivalent stresses in cortical and trabecular bones were evaluated with the same design program. RESULTS: The results were shown qualitatively and quantitatively by standard scales for each type of bone. By the results obtained, it can be suggested that positioning the implant completely in trabecular bone brings harm with respect to the generated stresses. Its implantation in the cortical bone has advantages with respect to better anchoring and locking, reflecting a better dissipation of the stresses along the implant/bone interfaces. In addition, the search for anchoring the implant in its apical region in cortical bone is of great value to improve stabilization and consequently better stress distribution. CONCLUSIONS: The implant position slightly below the bone in relation to the bone crest brings advantages as the best long-term predictability with respect to the expected neck bone loss.

Un'applicazione della teoria di Morse alla topologia delle varietà di Stein

In questa tesi si è data una dimostrazione dovuta ad Andreotti e Frenkel del Teorema di Lefschetz, utilizzando gli strumenti e i risultati della Teoria di Morse.

Teoria di Morse

Introduzione allo studio dell'omotopia di varietà differenziabili in relazione ai punti critici di funzioni di Morse definite su di esse con particolare attenzione al cambiamento di omotopia dell'insieme di sottolivello al passaggio di un valore critico. Applicazione al complesso di catene di Morse-Smale-Witten e dimostrazione dell'equivalenza tra l'omologia definita da questo complesso e l'omologia classica.

Cyclic automorphic graph decompositions

Chapter 1 introduces the tools and mechanics necessary for this report. Basic definitions and topics of graph theory which pertain to the report and discussion of automorphic decompositions will be covered in brief detail. An automorphic decomposition D of a graph H by a graph G is a G-decomposition of H such that the intersection of graph (D) @H. H is called the automorhpic host, and G is the automorphic divisor. We seek to find classes of graphs that are automorphic divisors, specifically ones generated cyclically. Chapter 2 discusses the previous work done mainly by Beeler. It also discusses and gives in more detail examples of automorphic decompositions of graphs. Chapter 2 also discusses labelings and their direct relation to cyclic automorphic decompositions. We show basic classes of graphs, such as cycles, that are known to have certain labelings, and show that they also are automorphic divisors. In Chapter 3, we are concerned with 2-regular graphs, in particular rCm, r copies of the m-cycle. We seek to show that rCm has a ρ-labeling, and thus is an automorphic divisor for all r and m. we discuss methods including Skolem type difference sets to create cycle systems and their correlation to automorphic decompositions. In the Appendix, we give classes of graphs known to be graceful and our java code to generate ρ-labelings on rCm.

Enumeration of inequivalent cycle decompositions

A k-cycle decomposition of order n is a partition of the edges of the complete graph on n vertices into k-cycles. In this report a backtracking algorithm is developed to count the number of inequivalent k-cycle decompositions of order n.

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.

Using the Morse Potential to Understand Reaction Coördinates using Maple

The interactions employed in the “linear” reaction A(g)+BC(g) -> AB(g) + C(g) in a “one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum path on the surface created.“one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum path on the surface created.

Planar point sets with large minimum convex decompositions

We show the existence of sets with n points (n ? 4) for which every convex decomposition contains more than (35/32)n?(3/2) polygons,which refutes the conjecture that for every set of n points there is a convex decomposition with at most n+C polygons. For sets having exactly three extreme pointswe show that more than n+sqr(2(n ? 3))?4 polygons may be necessary to form a convex decomposition.

Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups.

We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We also compare those results with the well-known characterizations for classical Besov spaces Bp,qs.

Kinetic study of the decompositions involved in the thermal degradation of commercial azodicarbonamide

The transitions and reactions involved in the thermal treatment of several commercial azodicarbonamides (ADC) in an inert atmosphere have been studied by dynamic thermogravimetry analysis (TGA), mass spectrometry and Fourier transform infrared (FTIR) spectroscopy. A pseudo-mechanistic model, involving several competitive and non-competitive reactions, has been suggested and applied to the correlation of the weight loss data. The model applied is capable of accurately representing the different processes involved, and can be of great interest in the understanding and quantification of such phenomena, including the simulation of the instantaneous amount of gases evolved in a foaming process. In addition, a brief discussion on the methodology related to the mathematical modeling of TGA data is presented, taking into account the complex thermal behaviour of the ADC.