Surface plasmon resonanceSurface plasmon resonance (SPR) is a phenomenon that occurs where electrons in a thin metal sheet become excited by light that is directed to the sheet with a particular angle of incidence, and then travel parallel to the sheet. Assuming a constant light source wavelength and that the metal sheet is thin, the angle of incidence that triggers SPR is related to the refractive index of the material and even a small change in the refractive index will cause SPR to not be observed.
Surface plasmonSurface plasmons (SPs) are coherent delocalized electron oscillations that exist at the interface between any two materials where the real part of the dielectric function changes sign across the interface (e.g. a metal-dielectric interface, such as a metal sheet in air). SPs have lower energy than bulk (or volume) plasmons which quantise the longitudinal electron oscillations about positive ion cores within the bulk of an electron gas (or plasma). The charge motion in a surface plasmon always creates electromagnetic fields outside (as well as inside) the metal.
Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Prostate-specific antigenProstate-specific antigen (PSA), also known as gamma-seminoprotein or kallikrein-3 (KLK3), P-30 antigen, is a glycoprotein enzyme encoded in humans by the KLK3 gene. PSA is a member of the kallikrein-related peptidase family and is secreted by the epithelial cells of the prostate gland. PSA is produced for the ejaculate, where it liquefies semen in the seminal coagulum and allows sperm to swim freely. It is also believed to be instrumental in dissolving cervical mucus, allowing the entry of sperm into the uterus.
Localized surface plasmonA localized surface plasmon (LSP) is the result of the confinement of a surface plasmon in a nanoparticle of size comparable to or smaller than the wavelength of light used to excite the plasmon. When a small spherical metallic nanoparticle is irradiated by light, the oscillating electric field causes the conduction electrons to oscillate coherently. When the electron cloud is displaced relative to its original position, a restoring force arises from Coulombic attraction between electrons and nuclei.
Diagonalizable matrixIn linear algebra, a square matrix is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix and a diagonal matrix such that , or equivalently . (Such , are not unique.) For a finite-dimensional vector space , a linear map is called diagonalizable if there exists an ordered basis of consisting of eigenvectors of .
Multi-parametric surface plasmon resonanceMulti-parametric surface plasmon resonance (MP-SPR) is based on surface plasmon resonance (SPR), an established real-time label-free method for biomolecular interaction analysis, but it uses a different optical setup, a goniometric SPR configuration. While MP-SPR provides same kinetic information as SPR (equilibrium constant, dissociation constant, association constant), it provides also structural information (refractive index, layer thickness). Hence, MP-SPR measures both surface interactions and nanolayer properties.
Surface plasmon polaritonSurface plasmon polaritons (SPPs) are electromagnetic waves that travel along a metal–dielectric or metal–air interface, practically in the infrared or visible-frequency. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal ("surface plasmon") and electromagnetic waves in the air or dielectric ("polariton"). They are a type of surface wave, guided along the interface in much the same way that light can be guided by an optical fiber.
Hermitian matrixIn mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j: or in matrix form: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
Logarithm of a matrixIn mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to Lie theory since when a matrix has a logarithm then it is in an element of a Lie group and the logarithm is the corresponding element of the vector space of the Lie algebra.
ProstateThe prostate (ˈprɒs.teɪt) is both an accessory gland of the male reproductive system and a muscle-driven mechanical switch between urination and ejaculation. It is found in all male mammals. It differs between species anatomically, chemically, and physiologically. Anatomically, the prostate is found below the bladder, with the urethra passing through it. It is described in gross anatomy as consisting of lobes and in microanatomy by zone. It is surrounded by an elastic, fibromuscular capsule and contains glandular tissue, as well as connective tissue.
Invertible matrixIn linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.
PlasmonIn physics, a plasmon is a quantum of plasma oscillation. Just as light (an optical oscillation) consists of photons, the plasma oscillation consists of plasmons. The plasmon can be considered as a quasiparticle since it arises from the quantization of plasma oscillations, just like phonons are quantizations of mechanical vibrations. Thus, plasmons are collective (a discrete number) oscillations of the free electron gas density. For example, at optical frequencies, plasmons can couple with a photon to create another quasiparticle called a plasmon polariton.
Prostate cancerProstate cancer is the uncontrolled growth of cells in the prostate, a gland in the male reproductive system just below the bladder. Early prostate cancer usually causes no symptoms. As the tumor grows, it can damage nearby organs causing erectile dysfunction, blood in the urine or semen, and trouble urinating. Some tumors eventually spread to other areas of the body, particularly the bones and lymph nodes. There, tumors cause severe bone pain, leg weakness or paralysis, and eventually death.
Matrix ringIn abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication . The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and Rn×n). Some sets of infinite matrices form infinite matrix rings. Any subring of a matrix ring is a matrix ring. Over a rng, one can form matrix rngs. When R is a commutative ring, the matrix ring Mn(R) is an associative algebra over R, and may be called a matrix algebra.
Prostatic acid phosphataseProstatic acid phosphatase (PAP), also prostatic specific acid phosphatase (PSAP), is an enzyme produced by the prostate. It may be found in increased amounts in men who have prostate cancer or other diseases. The highest levels of acid phosphatase are found in metastasized prostate cancer. Diseases of the bone, such as Paget's disease or hyperparathyroidism, diseases of blood cells, such as sickle-cell disease or multiple myeloma or lysosomal storage diseases, such as Gaucher's disease, will show moderately increased levels.
Analytic function of a matrixIn mathematics, every analytic function can be used for defining a matrix function that maps square matrices with complex entries to square matrices of the same size. This is used for defining the exponential of a matrix, which is involved in the closed-form solution of systems of linear differential equations. There are several techniques for lifting a real function to a square matrix function such that interesting properties are maintained. All of the following techniques yield the same matrix function, but the domains on which the function is defined may differ.
Tumor markerA tumor marker is a biomarker found in blood, urine, or body tissues that can be elevated by the presence of one or more types of cancer. There are many different tumor markers, each indicative of a particular disease process, and they are used in oncology to help detect the presence of cancer. An elevated level of a tumor marker can indicate cancer; however, there can also be other causes of the elevation (false positive values). Tumor markers can be produced directly by the tumor or by non-tumor cells as a response to the presence of a tumor.
BiosensorA biosensor is an analytical device, used for the detection of a chemical substance, that combines a biological component with a physicochemical detector. The sensitive biological element, e.g. tissue, microorganisms, organelles, cell receptors, enzymes, antibodies, nucleic acids, etc., is a biologically derived material or biomimetic component that interacts with, binds with, or recognizes the analyte under study. The biologically sensitive elements can also be created by biological engineering.
Benign prostatic hyperplasiaBenign prostatic hyperplasia (BPH), also called prostate enlargement, is a noncancerous increase in size of the prostate gland. Symptoms may include frequent urination, trouble starting to urinate, weak stream, inability to urinate, or loss of bladder control. Complications can include urinary tract infections, bladder stones, and chronic kidney problems. The cause is unclear. Risk factors include a family history, obesity, type 2 diabetes, not enough exercise, and erectile dysfunction.
