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2017

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Articles 10981 - 11010 of 12521

Full-Text Articles in Physical Sciences and Mathematics

Designing 2d Interfaces For 3d Gesture Retrieval Utilizing Deep Learning, Spencer Southard Jan 2017

Designing 2d Interfaces For 3d Gesture Retrieval Utilizing Deep Learning, Spencer Southard

UNF Graduate Theses and Dissertations

Gesture retrieval can be defined as the process of retrieving the correct meaning of the hand movement from a pre-assembled gesture dataset. The purpose of the research discussed here is to design and implement a gesture interface system that facilitates retrieval for an American Sign Language gesture set using a mobile device. The principal challenge discussed here will be the normalization of 2D gestures generated from the mobile device interface and the 3D gestures captured from video samples into a common data structure that can be utilized by deep learning networks. This thesis covers convolutional neural networks and auto encoders …


Impact Of Linear Disturbances On A Discontinuous Permafrost Peatland Environment, Michael Braverman Jan 2017

Impact Of Linear Disturbances On A Discontinuous Permafrost Peatland Environment, Michael Braverman

Theses and Dissertations (Comprehensive)

Permafrost is ground that remains at or below 0°C for at least two consecutive years (PIWP, 2012). In the continuous permafrost zone its thickness may exceed 300 m, in lower latitudes, permafrost thickness is progressively decreasing, its occurrence becomes discontinuous and eventually sporadic (PIWP, 2012). At the southern fringe of permafrost in northwestern Canada, just about few meters. In subarctic peatlands permafrost is one of the main elements governing the hydrological processes. Being very thin and with temperature just fractions of the degree below 0oC, it is very vulnerable to any changes in soil temperature and water content. …


Size And Shape Control In Metal Nanoparticles And Nanocomposites, Tomendro Subedi Jan 2017

Size And Shape Control In Metal Nanoparticles And Nanocomposites, Tomendro Subedi

Theses and Dissertations (Comprehensive)

This thesis describes major findings on the shape transformation of the precursor silver decahedral nanoparticles (AgDeNPs) with pentagonal symmetry and twin defects into silver pentagonal prism nanoparticles (AgPPNPs) using Br¯ as a shape selective reagent. Silica-encapsulation of the gold-plated AgDeNPs was also carried out forming ordered arrays of silica encapsulated gold-plated AgDeNPs (SiO2@Au@AgDeNPs) of different sizes. At first, synthetic procedures for AgDeNPs (pentagonal bipyramids), silver pentagonal rod nanoparticles (AgPRNPs) and gold-plating of AgDeNPs (Au@AgDeNPs) were optimized. Gold plating enhances the chemical stability of AgDeNPs and preserves the superior plasmonic properties of silver. This thesis deals with the transformation …


Spatial Distributions Of Tropical Cyclone Tornadoes By Intensity And Size Characteristics, Todd W. Moore Ph.D., Nicholas J. Sokol, Robert A. Blume Jan 2017

Spatial Distributions Of Tropical Cyclone Tornadoes By Intensity And Size Characteristics, Todd W. Moore Ph.D., Nicholas J. Sokol, Robert A. Blume

Geosciences Faculty Publications

Tropical cyclones that make landfall often spawn tornadoes. Previous studies have shown that these tornadoes are not uniformly distributed in the United States or in the tropical cyclone environment. They show that tornadoes tend to occur relatively close to the coastline and that they tend to cluster to the east-of-center in the tropical cyclone environment, particularly in the northeast and east-of-center quadrants. This study contributes to these studies by analyzing the spatial distributions of tropical cyclone tornadoes by intensity, path length, path width, and the damage potential index. The analyses confirm that most tornadoes occur relatively close to the coastline, …


Evolving Art: Modifying Context Free Art With A Genetic Algorithm, Marina Kent Jan 2017

Evolving Art: Modifying Context Free Art With A Genetic Algorithm, Marina Kent

Scripps Senior Theses

Context Free Design Grammar (CFDG) is a programming language for defining recursive structures that can be used to create art. I use CFDG as a design space for genetic programming, experimenting with various options for crossover, mutation, and fitness. In this exploratory work, multiple generations are manually assessed to determine the usefulness of the mutation strategies and fitness functions. I find that simple value mutation and fitness that alters general program structure is not enough to produce an increase of interesting images in CFDG. I discuss these findings as well as future avenues of inquiry for genetic programming in artistic …


G:, Taylor Lafe Cantrall Jan 2017

G:, Taylor Lafe Cantrall

Senior Projects Spring 2017

Senior Project submitted to The Division of Languages and Literature of Bard College.


Path From Paper To Paperless At Abana O&P, Stephanie Lutfallah Jan 2017

Path From Paper To Paperless At Abana O&P, Stephanie Lutfallah

Honors Theses

No abstract provided.


Predictive Modeling Of Functional Materials For Catalytic And Sensor Applications, Takat Rawal Jan 2017

Predictive Modeling Of Functional Materials For Catalytic And Sensor Applications, Takat Rawal

Electronic Theses and Dissertations

The research conducted in my dissertation focuses on theoretical and computational studies of the electronic and geometrical structures, and the catalytic and optical properties of functional materials in the form of nano-structures, extended surfaces, two-dimensional systems and hybrid structures. The fundamental aspect of my research is to predict nanomaterial properties through ab-initio calculations using methods such as quantum mechanical density functional theory (DFT) and kinetic Monte Carlo simulation, which help rationalize experimental observations, and ultimately lead to the rational design of materials for the electronic and energy-related applications. Focusing on the popular single-layer MoS2, I first show how its hybrid …


Groundwater Modeling For Assessing The Impacts Of Natural Hazards In East-Central Florida, Han Xiao Jan 2017

Groundwater Modeling For Assessing The Impacts Of Natural Hazards In East-Central Florida, Han Xiao

Electronic Theses and Dissertations

In coastal east-central Florida (ECF) , the low-lying coastal alluvial plains and barrier islands have a high risk of being inundated by seawater due to climate change effects such as sea-level rise, changing rainfall patterns, and intensified storm surge from hurricanes., This will produce saltwater intrusion into the coastal aquifer from infiltration of overtopping saltwater. In the inland ECF region, sinkhole occurrence is recognized as the primary geologic hazard causing massive financial losses to society in the past several decades. The objectives of this dissertation are to: (1) evaluate the impacts of sea-level rise and intensified storm surge on the …


Structure Evolution And Multiferroic Properties In Cobalt Doped Bi4Ndti3Fe1-XCoXO15- Bi3Ndti2Fe1-XCoxo12-Δ Intergrowth Aurivillius Compounds, D. L. Zhang, W. C. Huang, Z. W. Chen, W. B. Zhao, L. Feng, M. Li, Y. W. Yin, S. N. Dong, X. G. Li Jan 2017

Structure Evolution And Multiferroic Properties In Cobalt Doped Bi4Ndti3Fe1-XCoXO15- Bi3Ndti2Fe1-XCoxo12-Δ Intergrowth Aurivillius Compounds, D. L. Zhang, W. C. Huang, Z. W. Chen, W. B. Zhao, L. Feng, M. Li, Y. W. Yin, S. N. Dong, X. G. Li

Department of Physics and Astronomy: Faculty Publications

Here, we report the structure evolution, magnetic and ferroelectric properties in Co-doped 4- and 3-layered intergrowth Aurivillius compounds Bi4NdTi3Fe1-x CoxO15-Bi3NdTi2Fe1-xCoxO12-δ. The compounds suffer a structure evolution from the parent 4-layered phase (Bi4NdTi3FeO15) to 3-layered phase (Bi3NdTi2CoO12-δ) with increasing cobalt doping level from 0 to 1. Meanwhile the remanent magnetization and polarization show opposite variation tendencies against the doping level, and the sample with x = …


A Cobalt-Containing Eukaryotic Nitrile Hydratase, Salette Martinez, Xinhang Yang, Brian Bennett, Richard C. Holz Jan 2017

A Cobalt-Containing Eukaryotic Nitrile Hydratase, Salette Martinez, Xinhang Yang, Brian Bennett, Richard C. Holz

Physics Faculty Research and Publications

Nitrile hydratase (NHase), an industrially important enzyme that catalyzes the hydration of nitriles to their corresponding amides, has only been characterized from prokaryotic microbes. The putative NHase from the eukaryotic unicellular choanoflagellate organism Monosiga brevicollis (MbNHase) was heterologously expressed in Escherichia coli. The resulting enzyme expressed as a single polypeptide with fused α- and β-subunits linked by a seventeen-histidine region. Size-exclusion chromatography indicated that MbNHase exists primarily as an (αβ)2 homodimer in solution, analogous to the α2β2 homotetramer architecture observed for prokaryotic NHases. The NHase enzyme contained its full complement of Co(III) …


Quantitative Analysis Of Tobacco-Specific Nitrosamines And Their Precursor Alkaloids In Tobacco Extracts, Celeste T. Wilkinson Jan 2017

Quantitative Analysis Of Tobacco-Specific Nitrosamines And Their Precursor Alkaloids In Tobacco Extracts, Celeste T. Wilkinson

Theses and Dissertations

Tobacco-specific nitrosamines (TSNA) are carcinogenic constituents derived from alkaloids in tobacco. Researchers are actively exploring several avenues to reduce TSNA levels in tobacco products like moist snuff tobacco. The focus of the research presented within is the quantitative analysis of TSNA in tobacco, specifically N’-nitrosonornicotine (NNN), 4-(methylnitrosamino)-1(3-pyridyl)-1-butanone (NNK), N’-nitrosoanatabine (NAT), and N’-nitrosoanabasine (NAB).

Tobacco alkaloids and nitrosamines in tobacco are currently analyzed by different instrumentation due to orders of magnitude difference in their concentrations, chromatographic separation challenges due to structural similarities, and similar mass fragmentation patterns. An analytical column using silica and 1,2-bis(siloxy)ethane hybrid particles of 1.7 µm size is …


Comparing The Structural Components Variance Estimator And U-Statistics Variance Estimator When Assessing The Difference Between Correlated Aucs With Finite Samples, Anna L. Bosse Jan 2017

Comparing The Structural Components Variance Estimator And U-Statistics Variance Estimator When Assessing The Difference Between Correlated Aucs With Finite Samples, Anna L. Bosse

Theses and Dissertations

Introduction: The structural components variance estimator proposed by DeLong et al. (1988) is a popular approach used when comparing two correlated AUCs. However, this variance estimator is biased and could be problematic with small sample sizes.

Methods: A U-statistics based variance estimator approach is presented and compared with the structural components variance estimator through a large-scale simulation study under different finite-sample size configurations.

Results: The U-statistics variance estimator was unbiased for the true variance of the difference between correlated AUCs regardless of the sample size and had lower RMSE than the structural components variance estimator, providing better type 1 error …


Big Data Visualization Platform For Mixed Reality, Aliakbar Panahi Jan 2017

Big Data Visualization Platform For Mixed Reality, Aliakbar Panahi

Theses and Dissertations

The visualization of data helps to provide faster and deeper insight into the data. In this work, a system for visualizing and analyzing big data in an interactive mixed reality environment is proposed. Such a system can be used for representing different types of data such as temporal, geospatial, network graph, and high dimensional. Also, an implementation of this system for four different data types are created. The data types include network data, volumetric data, high dimensional, and spectral data for different mixed reality devices such as Microsoft HoloLens, Oculus Rift, Samsung Gear VR, and Android ARCore were created. It …


Using Strontium Isotopes In Conjunction With Major, And Trace Elements To Identify Water/Rock Interaction In The Upper Kittitas County, Washington, James Patterson, Carey Gazis Jan 2017

Using Strontium Isotopes In Conjunction With Major, And Trace Elements To Identify Water/Rock Interaction In The Upper Kittitas County, Washington, James Patterson, Carey Gazis

All Master's Theses

The complex bedrock lithologies in the Upper Kittitas County provide an ideal setting for developing isotopic methodology to identify groundwater sources and track flow paths through water-rock interaction. A wide range of 87Sr/86Sr (0.7040 to 0.7068) in surface waters, springs, and groundwater from wells was found, allowing for identification of the individual signatures of lithologic units. Rock leachates from different lithology were compared to water samples to determine a general 87Sr/86Sr signature of the water-rock interaction for that lithology. The signatures identified were systematically lower than their associated waters, but similar enough to identify the expected 87Sr/86Sr of water-rock interaction …


Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri Jan 2017

Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri

Theses and Dissertations

miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …


Parametric, Nonparametric And Semiparametric Approaches In Profile Monitoring Of Poisson Data, Sepehr Piri Jan 2017

Parametric, Nonparametric And Semiparametric Approaches In Profile Monitoring Of Poisson Data, Sepehr Piri

Theses and Dissertations

Profile monitoring is a relatively new approach in quality control best used when the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or nonlinear profiles under the assumption of the correct model specification. Our work considers those cases where the parametric model for the family of profiles is unknown or, at least uncertain. Consequently, we consider monitoring Poisson profiles via three methods, a nonparametric (NP) method using penalized splines, a nonparametric (NP) method using wavelets and a semi parametric (SP) procedure that combines both parametric …


Light-Driven Hydrogen Production From Aqueous Solutions Based On A New Dubois-Type Nickel Catalyst, Y. Zhou, S. Yang, J. Huang Jan 2017

Light-Driven Hydrogen Production From Aqueous Solutions Based On A New Dubois-Type Nickel Catalyst, Y. Zhou, S. Yang, J. Huang

Chemistry Faculty Research and Publications

In this work, we report a new photocatalytic system that links multifunctional semiconductor nanocrystals with emerging water-soluble molecular catalysts made of earth-abundant elements for H2 generation [Ni(P2RN2R′)2(BF4)2]4−, R = Ph, R′ = [PhSO3] (NiS). This noble metal free hybrid exhibits remarkable catalytic activity with a turnover number of 511 for H2 production and a photon-to-H2 conversion efficiency of 12.5%. The mechanistic insight into such high efficiency in this photocatalytic system was examined using a combination of steady-state emission and time-resolved …


Three Sources Of Errors In The Ehrenfest Treatment Of Inelastic Scattering And Possible Ways Of Resolving Them, Alexander Semenov, Dmitri Babikov Jan 2017

Three Sources Of Errors In The Ehrenfest Treatment Of Inelastic Scattering And Possible Ways Of Resolving Them, Alexander Semenov, Dmitri Babikov

Chemistry Faculty Research and Publications

In order to identify the origin of possible errors in the mixed quantum/classical approach to inelastic scattering [A. Semenov and D. Babikov, J. Chem. Phys. 140, 044306 (2014) and A. Semenov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 141, 114304 (2014)], a simplified model is considered that consists of one intermolecular degree of freedom and two intramolecular states, coupled by a simple potential. For this system, analytic derivations are carried out to determine (i) the exact quantum mechanical solution of the inelastic scattering problem, (ii) a simplified version of it with all oscillatory terms neglected, and (iii) …


Redox And Spectroscopic Properties Of Iron Porphyrin Nitroxyl In The Presence Of Weak Acids, Md. Hafizur Rahman, Michael D. Ryan Jan 2017

Redox And Spectroscopic Properties Of Iron Porphyrin Nitroxyl In The Presence Of Weak Acids, Md. Hafizur Rahman, Michael D. Ryan

Chemistry Faculty Research and Publications

The spectroelectrochemistry and voltammetry of Fe(OEP) (NO) in the presence of substituted phenols was studied. Cyclic voltammetry showed that two closely spaced waves were observed for the reduction of Fe(OEP) (NO) in the presence of substituted phenols. The first wave was a single electron reduction under voltammetric conditions. The second wave was kinetically controlled, multielectron process. Visible spectroelectrochemistry of Fe(OEP) (NO) in the presence of substituted phenols showed that three species were present during the electrolysis. Additional spectroscopic studies indicated that the two reduction species were Fe(OEP) (HNO) and Fe(OEP)(H2NOH). The Fe(OEP) (HNO) species, which can be generated …


A Multi-Method Exploration Of The Genetic And Environmental Risks Contributing To Tobacco Use Behaviors In Young Adulthood, Elizabeth K. Do Jan 2017

A Multi-Method Exploration Of The Genetic And Environmental Risks Contributing To Tobacco Use Behaviors In Young Adulthood, Elizabeth K. Do

Theses and Dissertations

Tobacco use remains the leading preventable cause of morbidity and mortality in both the United States and worldwide. Twin and family studies have demonstrated that both genetic and environmental factors are important contributors to tobacco use behaviors. Understanding how genes, the environment, and their interactions is critical to the development of public health interventions that focus on the reduction of tobacco related morbidity and mortality. However, few studies have examined the transition from adolescent to young adulthood – the time when many individuals are experimenting with and developing patterns of tobacco use. This dissertation thesis seeks to provide a comprehensive …


Exploring The Effects Of Different Classroom Environments On The Learning Process. Synthesis Of Thiazole-Linked Porous Organic Polymers For Co2 Separation And Nitro-Aromatics Sensing., Davide D'Urbino Jan 2017

Exploring The Effects Of Different Classroom Environments On The Learning Process. Synthesis Of Thiazole-Linked Porous Organic Polymers For Co2 Separation And Nitro-Aromatics Sensing., Davide D'Urbino

Theses and Dissertations

When attempting to study the learning process of undergraduate chemistry student, the classroom and any interaction that take place within it constitute the social context of interest. By studying how different approaches can foster different classroom environments, it is possible to approach course design from an informed and scientifically sound perspective. Thus, it becomes necessary to identify and quantify the factors that have a positive or negative effect on the classroom environment. Social comparison concerns, comfort levels and self-efficacy have been shown to be social factors that affect each other as well as the learning process and have therefore been …


Preparation And Evaluation Techniques Of Porous Materials And Mixed Matrix Membranes For Targeted Co2 Separation Applications, Tsemre Tessema Jan 2017

Preparation And Evaluation Techniques Of Porous Materials And Mixed Matrix Membranes For Targeted Co2 Separation Applications, Tsemre Tessema

Theses and Dissertations

The use of porous sorbents for physisorptive capture of CO2 from gas mixtures has been deemed attractive due to the low energy penalty associated with recycling of such materials. Porous organic polymers (POPs) have emerged as promising candidates with potential in the treatment of pre- and post- fuel combustion processes to separate CO2 from gas mixtures. Concurrently, significant advances have been made in establishing calculation methods that evaluate the practicality of porous sorbents for targeted gas separation applications. However, these methods rely on single gas adsorption isotherms without accounting for the dynamic gas mixtures encountered in real-life applications. …


Development Of General Purpose Liquid Chromatography Simulator For The Exploration Of Novel Liquid Chromatographic Strategies, Lena N. Jeong Jan 2017

Development Of General Purpose Liquid Chromatography Simulator For The Exploration Of Novel Liquid Chromatographic Strategies, Lena N. Jeong

Theses and Dissertations

The method development process in liquid chromatography (LC) involves optimization of a variety of method parameters including stationary phase chemistry, column temperature, initial and final mobile phase compositions, and gradient time when gradient mobile phases are used. Here, a general simulation program to predict the results (i.e., retention time, peak width and peak shape) of LC separations, with the ability to study various complex chromatographic conditions is described. The simulation program is based on the Craig distribution model where the column is divided into discrete distance (Δz) and time (Δt) segments in a grid and is …


Saving The Physics Ii: Who Needs To Be Saved? It Depends On Your Metaphysics, Menas Kafatos Jan 2017

Saving The Physics Ii: Who Needs To Be Saved? It Depends On Your Metaphysics, Menas Kafatos

Mathematics, Physics, and Computer Science Faculty Articles and Research

Physics does not need to be saved. If anything, physics was rescued in the early twentieth century with the advancement of both the theories of relativity and quantum mechanics. What needs to be saved is our world outlook or metaphysics because how a society acts and develops depends on what its belief systems are. Here we explore how a new metaphysics where consciousness is fundamental might just be what modern societies need.


Electromechanical Instability In Silicone-And Acrylate-Based Dielectric Elastomers, Liang Jiang, Yanfen Shou, Shaojuan Chen, Jianwei Ma, Tony Betts, Stephen Jerrams Jan 2017

Electromechanical Instability In Silicone-And Acrylate-Based Dielectric Elastomers, Liang Jiang, Yanfen Shou, Shaojuan Chen, Jianwei Ma, Tony Betts, Stephen Jerrams

Articles

Electromechanical instability (EMI) is regarded as a significant factor in preventing dielectric elastomers (DEs) fromachieving large voltage-induced deformations. In this study, the strain-stiffening effect was used to control the occurrence of EMI in DEs. The results show that the stretching ratio required to provide a feasible strain-stiffening effect in silicone rubber (SR) was smaller than that needed for a commercial DE material, VHB 4910. The experimental data were compared with currently used models for the simulation of EMI in DEs. We found that EMI could be eliminated in the deformation of these elastomers when pre-stretching was used. Through the application …


Enhancement Of Dielectric Properties With The Addition Of Bromine And Dopamine Modified Barium Titanate Particles To Silicone Rubber, Liang Jiang, David Kennedy, Stephen Jerrams, Tony Betts Jan 2017

Enhancement Of Dielectric Properties With The Addition Of Bromine And Dopamine Modified Barium Titanate Particles To Silicone Rubber, Liang Jiang, David Kennedy, Stephen Jerrams, Tony Betts

Articles

Dual-coated barium titanate (BT) particles were prepared using dopamine (DP) in conjunction with bromine (Br) in order to enhance the dielectric constant of silicone rubber (SR) composites containing evenly distributed BT particles. The results showed that both DP and Br were deposited on the BT particles. The dielectric constant of the SR/BT composite was significantly increased from 3.6 to 4.7 at 1 kHz with the addition of BT modified with dopamine (DP–BT). Moreover, the dielectric constant further rose to 4.9 at 1 kHz when the DP–BT particle was grafted with bromine (Br–DP–BT).


Holocene Cyclic Records Of Ice-Rafted Debris And Sea Ice Variations On The East Greenland And Northwest Iceland Margins, D. A. Darby, J. T. Andrews, S. T. Belt, A. E. Jennings, P. Cabedo-Sanz Jan 2017

Holocene Cyclic Records Of Ice-Rafted Debris And Sea Ice Variations On The East Greenland And Northwest Iceland Margins, D. A. Darby, J. T. Andrews, S. T. Belt, A. E. Jennings, P. Cabedo-Sanz

OES Faculty Publications

The dynamics of the Greenland Ice Sheet and drift of sea ice from the Arctic Ocean reaching Denmark Strait are poorly constrained. We present data on the provenance of Fe oxide detrital grains from two cores in the Denmark Strait area and compare the Fe grain source data with other environmental proxies in order to document the variations and potential periodicities in ice-rafted debris delivery during the Holocene. Based on their Fe grain geochemistry, the sediments can be traced to East Greenland sources and to more distal sites around the Arctic Basin. On the Holocene time scales of the two …


Long And Short-Range Air Navigation On Spherical Earth, Nihad E. Daidzic Jan 2017

Long And Short-Range Air Navigation On Spherical Earth, Nihad E. Daidzic

International Journal of Aviation, Aeronautics, and Aerospace

Global range air navigation implies non-stop flight between any two airports on Earth. Such effort would require airplanes with the operational air range of at least 12,500 NM which is about 40-60% longer than anything existing in commercial air transport today. Air transportation economy requires flying shortest distance, which in the case of spherical Earth are Orthodrome arcs. Rhumb-line navigation has little practical use in long-range flights, but has been presented for historical reasons and for comparison. Database of about 50 major international airports from every corner of the world has been designed and used in testing and route validation. …


On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao Jan 2017

On Degree Bound For Syzygies Of Polynomial Invariants, Zhao Gao

Senior Independent Study Theses

Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring of G is given in [2]. We develop the theory of commutative algebra and give the proof from [2] that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.