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2014

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Articles 11341 - 11370 of 12299

Full-Text Articles in Physical Sciences and Mathematics

Alteration Mineral Mapping With Aster Data By Integration Of Coded Spectral Ratio Imaging And Som Neural Network Model, Mohammad Hassan Tayebi, Majid Hashemi Tangestani, Robert Keller Vincent Jan 2014

Alteration Mineral Mapping With Aster Data By Integration Of Coded Spectral Ratio Imaging And Som Neural Network Model, Mohammad Hassan Tayebi, Majid Hashemi Tangestani, Robert Keller Vincent

Turkish Journal of Earth Sciences

This study applied coded spectral ratio imaging and a self-organizing map (SOM) neural network model for subpixel classification of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data to map alteration minerals of the Masahim volcano, SE Iran. Spectra of samples were measured using a FieldSpec spectroradiometer, and were interpreted for finding key alteration minerals. Key minerals including sericite and kaolinite were selected. Thirty-six nonreciprocal spectral ratios of 9 ASTER reflective bands were created. Each spectral parameter (of 9 spectral bands and 36 spectral ratios) for the field and library mineral spectra was divided into deciles. Each decile of spectral …


Testing Of The Recently Developed Tectonomagmatic Discrimination Diagrams From Hydrothermally Altered Igneous Rocks Of 7 Geothermal Fields, Kailasa Pandarinath Jan 2014

Testing Of The Recently Developed Tectonomagmatic Discrimination Diagrams From Hydrothermally Altered Igneous Rocks Of 7 Geothermal Fields, Kailasa Pandarinath

Turkish Journal of Earth Sciences

Recently developed multidimensional tectonomagmatic discrimination diagrams based on log-ratio variables of chemical elements, discordant outlier-free databases, and probability-based boundaries have been shown to work better than the earlier diagrams. Hydrothermally altered drilled well rock cuttings obtained from different depths of geothermal fields were used to test these diagrams to compare the inferred tectonic setting with the expected one. In spite of the hydrothermal alteration effects, these diagrams provided the following expected tectonic settings: (1) an arc setting for Ahuachapán and Berlin geothermal fields, El Salvador; (2) a rift setting for Cerro Prieto geothermal field, Mexico, and Tendaho geothermal field, Afar …


Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford Jan 2014

Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford

Electronic Theses and Dissertations

Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …


Electrodeposition And Characterisation Of Copolymers Based On Pyrrole And 3,4-Ethylenedioxythiophene In Bmim Bf4 Using A Microcell Configuration, Lavinia Astratine, Edmond Magner, John Cassidy, Tony Betts Jan 2014

Electrodeposition And Characterisation Of Copolymers Based On Pyrrole And 3,4-Ethylenedioxythiophene In Bmim Bf4 Using A Microcell Configuration, Lavinia Astratine, Edmond Magner, John Cassidy, Tony Betts

Articles

Electrochemical copolymerization of pyrrole (Py) and 3,4-ethylenedioxythiophene (EDOT) was performed in an ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate, (BMIM BF4) employing a ‘micro-cell’ in order to use the materials efficiently. Characterization of the copolymers formed on an ITO substrate was performed for different Py: EDOT ratios (1:2, 1:1, 2:1) in both aqueous and ionic liquid electrolytes. Electrochemical and spectroelectrochemical analysis revealed that the properties of the copolymer depend upon the Py/EDOT monomer ratio used. The copolymer PPy-co-PEDOT (2:1) displayed good stability, a switching time of 20 s and a colouration efficiency of 101.3 C-1cm2. The presence of Py in the copolymer stabilised …


Using Structure-Based Organic Chemistry Online Tutorials With 2 Automated Correction For Student Practice And Review, Timothy O'Sullivan, Gráinne Hargaden Jan 2014

Using Structure-Based Organic Chemistry Online Tutorials With 2 Automated Correction For Student Practice And Review, Timothy O'Sullivan, Gráinne Hargaden

Articles

This article describes the development and implementation of an open-access organic chemistry question bank for online tutorials and assessments at University College Cork and Technological University Dublin. SOCOT (structure-based organic chemistry online tutorials) may be used to supplement traditional small-group tutorials, thereby allowing students to develop essential problem-solving skills in organic chemistry. This online approach may be used for both formative and summative assessment. Students complete one problem set weekly or fortnightly, which consists of a number of questions of varying difficulty. A wide range of question types is possible; for example, prediction of reaction products, identification of reaction intermediates …


Varieties Of P-Restriction Semigroups, Peter R. Jones Jan 2014

Varieties Of P-Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The restriction semigroups, in both their one-sided and two-sided versions, have arisen in various fashions, meriting study for their own sake. From one historical perspective, as “weakly E-ample” semigroups, the definition revolves around a “designated set” of commuting idempotents, better thought of as projections. This class includes the inverse semigroups in a natural fashion. In a recent paper, the author introduced P-restriction semigroups in order to broaden the notion of “projection” (thereby encompassing the regular *-semigroups). That study is continued here from the varietal perspective introduced for restriction semigroups by V. Gould. The relationship between varieties of regular …


Master Regulators, Regulatory Networks, And Pathways Of Glioblastoma Subtypes, Serdar Bozdag, Aiguo Li, Mehmet Baysan, Howard A. Fine Jan 2014

Master Regulators, Regulatory Networks, And Pathways Of Glioblastoma Subtypes, Serdar Bozdag, Aiguo Li, Mehmet Baysan, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Glioblastoma multiforme (GBM) is the most common malignant brain tumor. GBM samples are classified into subtypes based on their transcriptomic and epigenetic profiles. Despite numerous studies to better characterize GBM biology, a comprehensive study to identify GBM subtype-specific master regulators, gene regulatory networks, and pathways is missing. Here, we used FastMEDUSA to compute master regulators and gene regulatory networks for each GBM subtype. We also ran Gene Set Enrichment Analysis and Ingenuity Pathway Analysis on GBM expression dataset from The Cancer Genome Atlas Project to compute GBM- and GBM subtype-specific pathways. Our analysis was able to recover some of the …


Recurrence Relations For Moments Of Dual Generalized Order Statistics From Weibull Gamma Distribution And Its Characterizations, M. A. W. Mahmoud, Y. Abdel-Aty, N. M. Mohamed, Gholamhossein Hamedani Jan 2014

Recurrence Relations For Moments Of Dual Generalized Order Statistics From Weibull Gamma Distribution And Its Characterizations, M. A. W. Mahmoud, Y. Abdel-Aty, N. M. Mohamed, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we establish explicit forms and new recurrence relations satisfied by the single and product moments of dual generalized order statistics from Weibull gamma distribution (WGD). The results include as particular cases the relations for moments of reversed order statistics and lower records. We present characterizations of WGD based on (i) recurrence relation for single moments, (ii) truncated moments of certain function of the variable and (iii) hazard function.


Monitoring The Influence Of Acid Deposition On Soil And Implications To Forest Health In The Daniel Boone National Forest, Tyler M. Sanderson Jan 2014

Monitoring The Influence Of Acid Deposition On Soil And Implications To Forest Health In The Daniel Boone National Forest, Tyler M. Sanderson

Theses and Dissertations--Forestry and Natural Resources

Combustion of fossil fuels has contributed to many environmental problems including acid deposition. The Clean Air Act (CAA) was created to reduce ecological problems by cutting emissions of sulfur and nitrogen. Reduced emissions and rainfall concentrations of acidic ions have been observed since the enactment of the CAA, but soils continue to receive some acid inputs. Soils sensitive to acid deposition have been found to have low pH, a loss of base cations and a shift in the mineral phase controlling the activity of Al3+ and/or SO42-. If inputs continue, soil may be depleted of base …


A Depth Refugium From Catastrophic Coral Bleaching Prevents Regional Extinction, Tyler B. Smith, Peter W. Glynn, Juan L. Maté, Lauren T. Toth, Joanna Gyory Jan 2014

A Depth Refugium From Catastrophic Coral Bleaching Prevents Regional Extinction, Tyler B. Smith, Peter W. Glynn, Juan L. Maté, Lauren T. Toth, Joanna Gyory

Ocean Engineering and Marine Sciences Faculty Publications

Species intolerant of changing climate might avoid extinction within refugia buffered from extreme conditions. Refugia have been observed in the fossil record but are not well documented or understood on ecological time scales. Using a 37-year record from the eastern Pacific across the two most severe El Nin˜ o events on record (1982–1983 and 1997– 1998) we show how an exceptionally thermally sensitive reef-building hydrocoral, Millepora intricata, twice survived catastrophic bleaching in a deeper-water refuge (.11 m depth). During both events, M. intricata was extirpated across its range in shallow water, but showed recovery within several years, while two other …


Comparing Biofouling Control Treatments For Use On Aquaculture Nets, Geoffrey Swain, Nagahiko Shinjo Jan 2014

Comparing Biofouling Control Treatments For Use On Aquaculture Nets, Geoffrey Swain, Nagahiko Shinjo

Ocean Engineering and Marine Sciences Faculty Publications

Test panels comprised of uncoated, copper coated and silicone coated 7/8'' (22 mm) mesh knitted nylon net were evaluated to compare their properties and the effectiveness to prevent biofouling. This paper describes test procedures that were developed to quantify the performance in terms of antifouling, cleanability, drag and cost. The copper treatment was the most effective at controlling fouling, however, the silicone treated nets were the easiest to clean. The drag forces on the net were a function of twine diameter, twine roughness and fouling. After immersion, the uncoated nets had the most drag followed by the silicone and copper …


Hp-Daemon: HIgh PErformance DIstributed ADaptive ENergy-Efficient MAtrix-MultiplicatiOn, Li Tan, Longxiang Chen, Zizhong Chen, Ziliang Zong, Rong Ge, Dong Li Jan 2014

Hp-Daemon: HIgh PErformance DIstributed ADaptive ENergy-Efficient MAtrix-MultiplicatiOn, Li Tan, Longxiang Chen, Zizhong Chen, Ziliang Zong, Rong Ge, Dong Li

Mathematics, Statistics and Computer Science Faculty Research and Publications

The demands of improving energy efficiency for high performance scientific applications arise crucially nowadays. Software-controlled hardware solutions directed by Dynamic Voltage and Frequency Scaling (DVFS) have shown their effectiveness extensively. Although DVFS is beneficial to green computing, introducing DVFS itself can incur non-negligible overhead, if there exist a large number of frequency switches issued by DVFS. In this paper, we propose a strategy to achieve the optimal energy savings for distributed matrix multiplication via algorithmically trading more computation and communication at a time adaptively with user-specified memory costs for less DVFS switches, which saves 7.5% more energy on average than …


Efficient Detection Of Counterfeit Products In Large-Scale Rfid Systems Using Batch Authentication Protocols, Farzana Rahman, Sheikh Iqbal Ahamed Jan 2014

Efficient Detection Of Counterfeit Products In Large-Scale Rfid Systems Using Batch Authentication Protocols, Farzana Rahman, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

RFID technology facilitates processing of product information, making it a promising technology for anti-counterfeiting. However, in large-scale RFID applications, such as supply chain, retail industry, pharmaceutical industry, total tag estimation and tag authentication are two major research issues. Though there are per-tag authentication protocols and probabilistic approaches for total tag estimation in RFID systems, the RFID authentication protocols are mainly per-tag-based where the reader authenticates one tag at each time. For a batch of tags, current RFID systems have to identify them and then authenticate each tag sequentially, one at a time. This increases the protocol execution time due to …


The Transmuted Marshall-Olkin Fréchet Distribution: Properties And Applications, Ahmed Z. Afify, Gholamhossein Hamedani, Indranil Ghosh, M. E. Mead Jan 2014

The Transmuted Marshall-Olkin Fréchet Distribution: Properties And Applications, Ahmed Z. Afify, Gholamhossein Hamedani, Indranil Ghosh, M. E. Mead

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper introduces a new four-parameter lifetime model, which extends the Marshall-Olkin Fréchet distribution introduced by Krishna et al. (2013), called the transmuted Marshall-Olkin Fréchet distribution. Various structural properties including ordinary and incomplete moments, quantile and generating function, Rényi and q-entropies and order statistics are derived. The maximum likelihood method is used to estimate the model parameters. We illustrate the superiority of the proposed distribution over other existing distributions in the literature in modeling two real life data sets.


Proxy-Based Reconstructions Of Earthquakes And Tsunamis At Quidico, South-Central Chile, Isabel J. Hong Jan 2014

Proxy-Based Reconstructions Of Earthquakes And Tsunamis At Quidico, South-Central Chile, Isabel J. Hong

All Master's Theses

We utilized geomorphic, microfossil, sedimentological, and stratigraphic methods to investigate the paleotsunami history at Quidico, Chile (38.1° S, 73.2° W). A combination of pits, cores, and riverbank exposures provide stratigraphic evidence of 8 sand layers at Quidico, including tsunami deposits from 2010 and 1960. The sands are laterally continuous but display landward thinning, disappearing completely from the stratigraphy 1.2 km inland from the coast. Intervening sediment layers consist of organicrich silts and peat. Grain size analysis shows the sand units are bimodal in distribution whereas the organic-rich silts and peat have a broader, bimodal distribution. Lithological analysis showed similarities among …


Spatial Relationship Between Gps Slip And Seismic Tremor During Cascadia Slow Slip Events, Hillary Lynn Goodner Jan 2014

Spatial Relationship Between Gps Slip And Seismic Tremor During Cascadia Slow Slip Events, Hillary Lynn Goodner

All Master's Theses

We model GPS deformation and timing of seismic tremor associated with transient deformation in Cascadia to test the hypothesis that tremor and slip occur synchronously but are spatially offset. For the period 2010–2013, we use seismic tremor data with a duration-moment relationship to predict GPS time series and compare them to observations. We find that observed GPS displacements are best predicted when tremor locations on the plate interface are shifted 15 km up-dip of their published epicenter. To test whether the spatial offset of tremor and slip is due to systematic mislocation of published epicenters, we attempt to identify individual …


Alpine And Other Abandoned Towns Along The Great Northern Railroad Near Stevens Pass, Washington, 1890-1930, Stacy Marie Stanley Jan 2014

Alpine And Other Abandoned Towns Along The Great Northern Railroad Near Stevens Pass, Washington, 1890-1930, Stacy Marie Stanley

All Master's Theses

Despite the wealth of research on the early transcontinental railroads of the West, including certain areas in Washington State, there is little known about the railroad towns, camps and logging communities that arose due to the construction of the Great Northern Railroad in the Stevens Pass area. This thesis summarizes some of the information on the history of the study area, as well as results of a field investigation of archaeological remnants of one railroad town, the town of Alpine. Alpine was a short-lived town established during construction of the railroad ca. 1892 or a little later in 1910, and …


Composition Of Integers With Bounded Parts, Darren B. Glass Jan 2014

Composition Of Integers With Bounded Parts, Darren B. Glass

Math Faculty Publications

In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function describing the number of k-tuples whose entries are bounded in this way and sum to a fixed value g.


A Multiwavelength View On The Dusty Wolf-Rayet Star Wr 48a, Svetozar A. Zhekov, Toma Tomov, Marcin P. Gawronski, Leonid N. Georgiev, Jura Borissova, Radostin Kurtev, Marc Gagne, Marcin Hajduk Jan 2014

A Multiwavelength View On The Dusty Wolf-Rayet Star Wr 48a, Svetozar A. Zhekov, Toma Tomov, Marcin P. Gawronski, Leonid N. Georgiev, Jura Borissova, Radostin Kurtev, Marc Gagne, Marcin Hajduk

Earth & Space Sciences Faculty Publications

No abstract provided.


X-Rays From Magnetic Massive Ob Stars, V. Petit, D. H. Cohen, Y. Naze´, Marc Gagne, R. H.D. Townsend, M. A. Leutenegger, A. Ud-Doula, S. P. Owocki, G. A. Wade Jan 2014

X-Rays From Magnetic Massive Ob Stars, V. Petit, D. H. Cohen, Y. Naze´, Marc Gagne, R. H.D. Townsend, M. A. Leutenegger, A. Ud-Doula, S. P. Owocki, G. A. Wade

Earth & Space Sciences Faculty Publications

No abstract provided.


Homoleptic Nickel(Ii) Complexes Of Redox-Tunable Pincer-Type Ligands, Jeewantha S. Hewage, Sarath Wanniarachchi, Tyler James Morin, Brendan J Liddle, Megan Banaszynski, Sergey V. Lindeman, Brian Bennett, James R. Gardinier Jan 2014

Homoleptic Nickel(Ii) Complexes Of Redox-Tunable Pincer-Type Ligands, Jeewantha S. Hewage, Sarath Wanniarachchi, Tyler James Morin, Brendan J Liddle, Megan Banaszynski, Sergey V. Lindeman, Brian Bennett, James R. Gardinier

Physics Faculty Research and Publications

Different synthetic methods have been developed to prepare eight new redox-active pincer-type ligands, H(X,Y), that have pyrazol-1-yl flanking donors attached to an ortho-position of each ring of a diarylamine anchor and that have different groups, X and Y, at the para-aryl positions. Together with four previously known H(X,Y) ligands, a series of 12 Ni(X,Y)2 complexes were prepared in high yields by a simple one-pot reaction. Six of the 12 derivatives were characterized by single-crystal X-ray diffraction, which showed tetragonally distorted hexacoordinate nickel(II) centers. The nickel(II) complexes exhibit two quasi-reversible one-electron oxidation waves in their cyclic voltammograms, with …


Degradation Of High Voltage Glass Fiber-Reinforced Polymer Matrix Composites By Aggressive Environmental Conditions, Tianyi Lu Jan 2014

Degradation Of High Voltage Glass Fiber-Reinforced Polymer Matrix Composites By Aggressive Environmental Conditions, Tianyi Lu

Electronic Theses and Dissertations

Polymer matrix composites reinforced with either E glass or ECR glass fibers-reinforced are used in a variety of high voltage electrical applications because of their advantages like lower weight and cost. However, they can be damaged by aggressive in-service conditions such as high temperature, ultraviolet radiation, moisture, ozone and corrosive environments. Different degradation mechanisms can develop in high voltage PMCs under those extreme environments, which, in turn, can affect the long term structural durability of the composites. A set of PMCs reinforced with ECR-glass and E-glass fibers embedded in four different resins has been investigated in this study. In addition, …


A Numerical Method For A Nonlinear Singularly Perturbed Interior Layer Problem Using An Approximate Layer Location, Jason Quinn Jan 2014

A Numerical Method For A Nonlinear Singularly Perturbed Interior Layer Problem Using An Approximate Layer Location, Jason Quinn

Articles

A class of nonlinear singularly perturbed interior layer problems is examined in this paper. Solutions exhibit an interior layer at an a priori unknown location. A numerical method is presented that uses a piecewise uniform mesh refined around approximations to the first two terms of the asymptotic expansion of the interior layer location. The first term in the expansion is used exactly in the construction of the approximation which restricts the range of problem data considered. The method is shown to converge point-wise to the true solution with a first order convergence rate (overlooking a logarithmic factor) for sufficiently small …


Complex Absorbing Potential Method For Dirac Operators. Clusters Of Resonances, Jimmy Kungsman, Michael Melgaard Jan 2014

Complex Absorbing Potential Method For Dirac Operators. Clusters Of Resonances, Jimmy Kungsman, Michael Melgaard

Articles

For both nonrelativistic and relativistic Hamiltonians, the Complex Absorbing Potential (CAP) method has been applied extensively to calculate resonances in Physics and Chemistry. We study clusters of resonances for the perturbed Dirac operator near the real axis and, in the semiclassical limit, we establish the CAP method rigorously by showing that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa.


Evaporation Screening, Scattering, And Quantum Tunneling Near The Horizons Of Schwarzschild And Reissner-Nordstroem Black Holes, Emil Prodanov Jan 2014

Evaporation Screening, Scattering, And Quantum Tunneling Near The Horizons Of Schwarzschild And Reissner-Nordstroem Black Holes, Emil Prodanov

Articles

For the radial motion of massive particles with large angular momenta in Schwarzschild geometry and that of massive charged particles with large
angular momenta or energy in a particular range in Reissner-Nordstroem geometry, there exist classically forbidden regions on the outside of
the respective event horizons which scatter certain in-falling geodesics or screen some of the black holes' evaporation by reflecting the emitted

particles back into the black holes. Quantum tunneling across this forbidden regions is studied.


Bergm: Bayesian Exponential Random Graphs In R, Alberto Caimo, Nial Friel Jan 2014

Bergm: Bayesian Exponential Random Graphs In R, Alberto Caimo, Nial Friel

Articles

In this paper we describe the main featuress of the Bergm package for the open-source R software which provides a comprehensive framework for Bayesian analysis for exponential random graph models: tools for parameter estimation, model selection and goodness-of-fit diagnostics. We illustrate the capabilities of this package describing the algorithms through a tutorial analysis of three network datasets.


New Insights On Free Energies And Saint-Venant’S Principle In Viscoelasticity, L. Diseri, G. Gentili, John Murrough Golden Jan 2014

New Insights On Free Energies And Saint-Venant’S Principle In Viscoelasticity, L. Diseri, G. Gentili, John Murrough Golden

Articles

This work was conceived in 1999 and brought near completion by 2003. Giorgio Gentili was deeply involved in this research until his untimely death. He is greatly missed. Work pressures on the other authors forced a postponement of research on this topic, originally envisaged as lasting a few months but in the event it turned out to be nearly ten years. We now dedicate this work to the memory of Giorgio and to his Family.


Noncovalent Interactions Involving Microsolvated Networks Of Trimethylamine N-Oxide, Kristina Andrea Cuellar Jan 2014

Noncovalent Interactions Involving Microsolvated Networks Of Trimethylamine N-Oxide, Kristina Andrea Cuellar

Electronic Theses and Dissertations

This thesis research focuses on the effects of the formation of hydrogen-bonded networks with the important osmolyte trimethylamine N-oxide (TMAO). Vibrational spectroscopy, in this case Raman spectroscopy, is used to interpret the effects of noncovalent interactions by solvation with select hydrogen bond donors such as water, methanol, ethanol and ethylene glycol in the form of slight changes in vibrational frequencies. Spectral shifts in the experimental Raman spectra of interacting molecules are compared to the results of electronic structure calculations on explicit hydrogen bonded molecular clusters. The similarities in the Raman spectra of microsolvated TMAO using a variety of hydrogen bond …


Moments Of Products Of L-Functions, Caroline Laroche Turnage-Butterbaugh Jan 2014

Moments Of Products Of L-Functions, Caroline Laroche Turnage-Butterbaugh

Electronic Theses and Dissertations

We first consider questions on the distribution of the primes. Using the recent advancement towards the Prime k-tuple Conjecture by Maynard and Tao, we show how to produce infinitely many strings of consecutive primes satisfying specified congruence conditions. We answer an old question of Erdös and Turán by producing strings of consecutive primes whose successive gaps form an increasing (respectively decreasing) sequence. We also show that such strings exist whose successive gaps follow a certain divisibility pattern. Finally, for any coprime integers a and D ≥ 1, we refine a theorem of D. Shiu and find strings of consecutive primes …


(Visible) Tilings Of Squares And Hypercubes, John Randall Burt Jan 2014

(Visible) Tilings Of Squares And Hypercubes, John Randall Burt

Electronic Theses and Dissertations

More than eighty years ago, Erdos considered sums of the side lengths of squares packed into a unit square.Here we consider various classes of tilings , this is, packings where there is no empty space inside the unit square. Several types of questions will be explored here. Various construction techniques are introduced, especially methods of generating tilings from tilings with fewer tiles. For some small values of n, I determine all tilings of the unit square with n tiles. I have found a best possible upper bound for a visible tiling, that is a tiling which every tile shares a …