Some Applications of Simons’ Inequality

We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

Using Video Analysis to Investigate Conservation Impulse and Mechanical Energy Laws

Video analysis provides an educational, motivating, and cost-effective alternative to traditional course- related activities in physics education. Our paper presents results from video analysis of experiments “Collision of balls” and “Motion of a ball rolled on inclined plane” as examples to illustrate the laws of conservation of impulse and mechanical energy.

Monte Carlo Study of Particle Transport Problem in Air Pollution

2002 Mathematics Subject Classification: 65C05.

Managua Relief

Bob del Toro, Dianne Haley and Others with Toys for Managuan Relief. On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum 887-3400. april 30, 1973. Cutlines: More than 350 dozens of various balls, skate boards and games were recently purchased by the Student Governance Committee of Florida International University for the young people of Managua, Nicaragua who not only do not have enough toys but are unable to attend schools which are closed. Left to right are, Bob del Toro, Dianne Haley, Chairman of the Student Governance Committee, Hialeah Councilman Jack Weaver of the Hialeah-Managua Sister City Committee, Barbara O'Nan and Margaret Klein.

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum From: City of Hialeah Publicity Bureu. 401 1/2 East 1st Ave. Hialeah, Fla. 887-3400. april 30, 1973. Cutlines: Florida International University students recently raised more than $ 1,000 for more than 300 dozens toys and balls for the youngsters of Managua, Nicaragua. With the balls above are shown student Committee members and oficials of the Hialeah-Managua Sister City Committee, left to rigth: Bob del Toro, Sister City Committe president Raymond R. Schultz, Student Governance Committee chairman Dianne Haley and Hialeah City councilman Jack Weaver.

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements by organizations were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum From: City of Hialeah Publicity Bureu. 401 1/2 East 1st Ave. Hialeah, Fla. 887-3400. april 30, 1973. Cutlines: Skate boards, paddle balls and flying saucers were among the big shipment of toys which was recently dispatched to Managua, Nicaragua by students of Florida International University through the Hialeah-Managua Sister Committee. Examining the toys above are, left to right: Margaret Klein, Hialeah councilman Jack Weaver and Barbara O'Nan.

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Managua Relief

On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Managua Relief

The Miami News. Mon., March 19, 1973. Managuan Relief. Miami News Staff Photo by George Kochaniec. Raymond and Connie Schultz with toys. (Back) "Focuses on kids" article On December 23, 12:29 a.m. local time in Managua, Nicaragua, a magnitude 6.2 earthquake occurred. The earth caused widespread damage among Managua, the capital city. In Managua, 5,000 residents were killed, 20,000 were injured and over 250,000 were left homeless. In Miami, residents and relief organizations focused on helping children. Wife of General Arturo Somoza pleaded on efforts on gathering sporting goods and toys for Managua’s young people. Relief committees purchased 230 dozen balls – basketball, rubber, and volley, soccer, and others. Nearly $500 came from students in Hialeah High School. Jump ropes and jacks were donated from a sorority at Florida International University. Arrangements were made to bring 44,000 pounds of baby formula and canned meat and 13,000 pounds of medicine. Many of Miami’s corporations, associations, and residents contributed to the Managuan Relief effort. Source: The Miami News, March 19, 1973 by Lynn Feigenbaum

Efeito da moagem de alta energia na densificação e microestrutura do compósito AI2O3-Cu

The Cu-Al2O3 composite ceramic combines the phase of alumina, which is extremely hard and durable, yet very brittle, to metallic copper phase high ductility and high fracture toughness. These characteristics make this material a strong candidate for use as a cutting tool. Al2O3-Cu composite powders nanocrystalline and high homogeneity can be produced by high energy milling, as well as dense and better mechanical structures can be obtained by liquid phase sintering. This work investigates the effect of high-energy milling the dispersion phase Al2O3, Cu, and the influence of the content of Cu in the formation of Cu-Al2O3 composite particles. A planetary mill Pulverisatte 7 high energy was used to perform the experiments grinding. Al2O3 powder and Cu in the proportion of 5, 10 and 15% by weight of Cu were placed in a container for grinding with balls of hard metal and ethyl alcohol. A mass ratio of balls to powder of 1:5 was used. All powders were milled to 100 hours, and powder samples were collected after 2, 10, 20, 50 and 70 hours of grinding. Composite powders with compact cylindrical shape of 8 mm diameter were pressed and sintered in uniaxial matrix resistive furnace to 1200, 1300 to 1350 °C for 60 minutes under an atmosphere of argon and hydrogen. The heating rate used was 10°C/min. The powders and structures of the sintered bodies were characterized by XRD, SEM and EDS. Analysis TG, DSC and particle size were also used to characterize the milled powders, as well as dilatometry was used to observe the contraction of the sintered bodies. The density of the green and sintered bodies was measured using the geometric method (mass / volume). Vickers microhardness with a load of 500 g for 10 s were performed on sintered structures. The Cu-Al2O3 composite with 5% copper density reached 61% of theoretical density and a hardness of 129 HV when sintered at 1300 ° C for 1h. In contrast, lower densities (59 and 51% of the theoretical density) and hardness (110 HV and 105) were achieved when the copper content increases to 10 and 15%.

Materiais bionanocompósitos a base de argilominerais e hidróxidos duplos lamelares como sistemas de liberação de fármacos

Bionanocomposites systems clay base (montmorillonite and sepiolite), layered double hidroxides and biopolymers (carboxymethylcellulose and zein) were evaluated as topical delivery systems with antibacterial activity and as oral delivery systems. For this study, neomycin, a topical antibiotic, indicated mainly for open wound infections. The drug amoxicillin, an antibiotic indicated mainly for throat infections, were also used in this study. Both antibiotics were used as model drugs. Initially, drugs were incorporated directly into the biopolymer matrix, comprising the combination of carboxymethylcellulos and zein, being conformed as movies and balls and evaluated for their antibacterial activity and controlled release simulating gastrointestinal fluids. Moreover, hybrids materials have been prepared where the neomycin drug was incorporated into the lamellar inorganic solids, such as montmorillonite by ion exchange reaction, and the fibrous type, such as sepiolite by adsorption in aqueous solution. But the drug amoxicillin was incorporated into layered double hydroxides by anion exchange and montmorillonite by cation exchange. The resulting hybrids were in turn combined with the biopolymer matrix yielding bionanocomposites shaped materials such as films were tested for their antibacterial activity, and the shaped materials beads were tested for their release in the gastrointestinal fluids. Through the analysis of various physico-chemical techniques, we observed the interactions between the studied materials, the formation of hybrids materials, obtaining the bionanocomposites materials and material efficiency when applied in controlled release of drugs both topical and use oral mainly influenced by the presence of zein, are promising as topical delivery systems and oral drugs.

An investigation into the tension arising between natural language and mathematical language experienced by mechanical engineering students

This investigation is grounded within the concept of embodied cognition where the mind is considered to be part of a biological system. A first year undergraduate Mechanical Engineering cohort of students was tasked with explaining the behaviour of three balls of different masses being rolled down a ramp. The explanations given by the students highlighted the cognitive conflict between the everyday interpretation of the word energy and its mathematical use. The results showed that even after many years of schooling, students found it challenging to interpret the mathematics they had learned and relied upon pseudo-scientific notions to account for the behaviour of the balls.

Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.