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Magic Angle
The magic angle is a precisely defined angle, the value of which is approximately 54.7356°. The magic angle is a root of a second-order Legendre polynomial, , and so any interaction which depends on this second-order Legendre polynomial vanishes at the magic angle. This property makes the magic angle of particular importance in magic angle spinning solid-state NMR spectroscopy. In magnetic resonance imaging, structures with ordered collagen, such as tendons and ligaments, oriented at the magic angle may appear hyperintense in some sequences; this is called the magic angle artifact or effect. Mathematical definition The magic angle ''θ''m is \theta_\mathrm = \arccos \frac = \arctan \sqrt \approx 0.955\,32\ \text \approx 54.7^\circ \! , where arccos and arctan are the inverse cosine and tangent functions respectively. is the angle between the space diagonal of a cube and any of its three connecting edges, see image. Another representation of the magic angle is half of the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Legendre Polynomial
In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. Closely related to the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, big q-Legendre polynomials, and associated Legendre functions. Definition and representation Definition by construction as an orthogonal system In this approach, the polynomials are defined as an orthogonal system with respect to the weight function w(x) = 1 over the interval 1,1/math>. That is, P_n(x) is a polynomial of degree n, such that \int_^1 P_m(x) P_n(x) \,dx = 0 \quad \text n \ne m. With the additional sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dipolar Coupling
In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways: * An electric dipole moment, electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system is a pair of charges of equal magnitude but opposite sign separated by some typically small distance. (A permanent electric dipole is called an electret.) * A magnetic dipole is the closed circulation of an electric current system. A simple example is a single loop of wire with constant current through it. A bar magnet is an example of a magnet with a permanent magnetic dipole moment. Dipoles, whether electric or magnetic, can be characterized by their dipole moment, a vector quantity. For the simple electric dipole, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges. (To be precis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nuclear Magnetic Resonance Spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a Spectroscopy, spectroscopic technique based on re-orientation of Atomic nucleus, atomic nuclei with non-zero nuclear spins in an external magnetic field. This re-orientation occurs with absorption of electromagnetic radiation in the radio frequency region from roughly 4 to 900 MHz, which depends on the Isotope, isotopic nature of the nucleus and increases proportionally to the strength of the external magnetic field. Notably, the resonance frequency of each NMR-active nucleus depends on its chemical environment. As a result, NMR spectra provide information about individual functional groups present in the sample, as well as about connections between nearby nuclei in the same molecule. As the NMR spectra are unique or highly characteristic to individual compounds and functional groups, NMR spectroscopy is one of the most important methods to identify ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hose
A hose is a flexible hollow tube or pipe designed to carry fluids from one location to another, often from a faucet or hydrant. Early hoses were made of leather, although modern hoses are typically made of rubber, canvas, and helically wound wire. Hoses may also be made from plastics such as polyvinyl chloride, polytetrafluoroethylene, and polyethylene terephthalate, or from metals such as stainless steel. See also * *Heated hose Heated hoses are hoses used for transporting liquids or molten materials where integral heat is needed for temperature control. Heated hoses are suitable for environments from -40°C to 80°C and can be used in explosion proof, explosion-proof zo ... References Further reading * Hydraulics {{tool-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Supraspinatus Tendinitis
Shoulder impingement syndrome is a syndrome involving tendonitis (inflammation of tendons) of the rotator cuff muscles as they pass through the subacromial space, the passage beneath the acromion. It is particularly associated with tendonitis of the supraspinatus muscle. This can result in pain, weakness, and loss of movement at the shoulder. Signs and symptoms The most common symptoms in impingement syndrome are pain, weakness and a loss of movement at the affected shoulder. The pain is often worsened by shoulder overhead movement and may occur at night, especially when lying on the affected shoulder. The onset of the pain may be acute if due to an injury or insidious if due to a gradual process such as an osteoarthritic spur. The pain has been described as dull rather than sharp, and lingers for long periods of time, making it hard to fall asleep. Other symptoms can include a grinding or popping sensation during movement of the shoulder. The range of motion at the shoulder may b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Rotator Cuff
The rotator cuff (SITS muscles) is a group of muscles and their tendons that act to stabilize the human shoulder and allow for its extensive range of motion. Of the seven scapulohumeral muscles, four make up the rotator cuff. The four muscles are: * supraspinatus muscle * infraspinatus muscle * teres minor muscle * subscapularis muscle. Structure Muscles composing rotator cuff The supraspinatus muscle spreads out in a horizontal band to insert on the superior facet of the greater tubercle of the humerus. The greater tubercle projects as the most Lateral (anatomy), lateral structure of the humeral head. Medial (anatomy), Medial to this, in turn, is the lesser tubercle of the humeral head. The subscapularis muscle Origin (anatomy), origin is divided from the remainder of the rotator cuff origins as it is deep to the scapula. The four tendons of these muscles converge to form the rotator cuff tendon. These tendinous Insertion (anatomy), insertions along with the articular cap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
MRI Sequence
An MRI pulse sequence in magnetic resonance imaging (MRI) is a particular setting of pulse sequences and pulsed field gradients, resulting in a particular image appearance. A multiparametric MRI is a combination of two or more sequences, and/or including Magnetic resonance imaging#Other specialized configurations, other specialized MRI configurations such as In vivo magnetic resonance spectroscopy, spectroscopy. Spin echo T1 and T2 Each tissue returns to its equilibrium state after excitation by the independent relaxation processes of T1 (Spin–lattice relaxation, spin-lattice; that is, magnetization in the same direction as the static magnetic field) and T2 (Spin-spin relaxation time, spin-spin; transverse to the static magnetic field). To create a T1-weighted image, magnetization is allowed to recover before measuring the MR signal by changing the repetition time (TR). This image weighting is useful for assessing the cerebral cortex, identifying fatty tissue, characteriz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In regular perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, often keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Magic Angle Spinning
In solid-state NMR spectroscopy, magic-angle spinning (MAS) is a technique routinely used to produce better resolution NMR spectra. MAS NMR consists in spinning the sample (usually at a frequency of 1 to 130 kHz) at the magic angle θm (ca. 54.74°, where cos2θm=1/3) with respect to the direction of the magnetic field. Three main interactions responsible in solid state NMR ( dipolar, chemical shift anisotropy, quadrupolar) often lead to very broad and featureless NMR lines. However, these three interactions in solids are orientation-dependent and can be averaged to some extent by MAS: * The nuclear dipolar interaction has a 3\cos^2\theta - 1 dependence, where \theta is the angle between the internuclear axis and the main magnetic field. As a result, the dipolar interaction vanish at the magic angle θm and the interaction contributing to the line broadening is removed. Even though all internuclear vectors cannot be all set to the magic angle, rotating the sample around ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Solid-state Nuclear Magnetic Resonance
Solid-state nuclear magnetic resonance (ssNMR) is a spectroscopy technique used to characterize atomic-level structure and dynamics in solid materials. ssNMR spectra are broader due to nuclear spin interactions which can be categorized as dipolar coupling, chemical shielding, quadrupolar interactions, and j-coupling. These interactions directly affect the lines shapes of experimental ssNMR spectra which can be seen in powder and dipolar patterns. There are many essential solid-state techniques alongside advanced ssNMR techniques that may be applied to elucidate the fundamental aspects of solid materials. ssNMR is often combined with magic angle spinning (MAS) to remove anisotropic interactions and improve the sensitivity of the technique. The applications of ssNMR further extend to biology and medicine. Nuclear spin interactions The resonance frequency of a nuclear spin depends on the strength of the magnetic field at the nucleus, which can be modified by isotropic (e.g. c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Chemical Shift Anisotropy
In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of a molecule. Chemical shifts are also used to describe signals in other forms of spectroscopy such as photoemission spectroscopy. Some atomic nuclei possess a magnetic moment (nuclear spin), which gives rise to different energy levels and resonance frequencies in a magnetic field. The total magnetic field experienced by a nucleus includes local magnetic fields induced by currents of electrons in the molecular orbitals (electrons have a magnetic moment themselves). The electron distribution of the same type of nucleus (e.g. ) usually varies according to the local geometry (binding partners, bond lengths, angles between bonds, and so on), and with it the local magnetic field at each nucleus. This is reflected in the spin energy levels (and re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. High-resolution nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crysta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
