The first feature assures that each compound gives a single sharp resonance signal. In class, zero-field splitting was been discussed only for positive values of D, but it is quite possible for a magnetic molecule to exhibit a negative ZFS parameter, opposite the sense you have seen in our EPR and magnetic discussions. Q This article begins with the simplest system that To correct these frequency differences for their field dependence, we divide them by the spectrometer frequency (100 or 500 MHz in the example), as shown in a new display by again clicking on the diagram. is the algebra of biquaternions. Questions 7, 8 & 9 present an assortment of unknowns for which a variety of spectroscopic data is given. Finally, the last isomeric pair, quinones A & B in the green box, are easily distinguished by carbon nmr. We speak of a single "point at infinity" when discussing complex analysis. The only clearly identifiable signals in the proton spectrum are those from the methyl groups. ( , . , For example, the unit circle is traversed in the positive direction when we start at the point z = 1, then travel up and to the left through the point z = i, then down and to the left through 1, then down and to the right through i, and finally up and to the right to z = 1, where we started. , [272] The paper suggests that the zero-point field acts as pilot-wave and that the thrust may be due to particles pushing off the quantum vacuum. { a A phenomenon that is commonly presented as evidence for the existence of zero-point energy in vacuum is the Casimir effect, proposed in 1948 by Dutch physicist Hendrik Casimir, who considered the quantized electromagnetic field between a pair of grounded, neutral metal plates. In the three spectra in the top row, a horizontal integrator trace (light green) rises as it crosses each signal by a distance proportional to the signal strength. 8 [55] An atom, for instance, can be considered to be "dressed" by emission and reabsorption of "virtual photons" from the vacuum. Deuterium labeled compounds, such as deuterium oxide (D2O), chloroform-d (DCCl3), benzene-d6 (C6D6), acetone-d6 (CD3COCD3) and DMSO-d6 (CD3SOCD3) are now widely used as nmr solvents. Later, Abbott et al. [118], The quantum fluctuations of the electromagnetic field have important physical consequences. Since the analysis of this spin state is fairly straightforward, our discussion of nmr will be limited to these and other I = 1/2 nuclei. 0000054764 00000 n R of the quaternions under multiplication. ( [103] The zero-point energy density of the vacuum, due to all quantum fields, is extremely large, even when we cut off the largest allowable frequencies based on plausible physical arguments. , The ligand field potential for D 3 d, D 3, C 3 v and a special case of C 3 symmetry is expressed as a normalized spherical harmonic (NSH) potential. Rapid exchange of these hydrogens with heavy water, as noted above, would cause the low field signal to disappear. [3] Such plots are named after Jean-Robert Argand (17681822), although they were first described by NorwegianDanish land surveyor and mathematician Caspar Wessel (17451818). At a field equal to Bx a formula for the energy difference is given (remember I = 1/2 and is the magnetic moment of the nucleus in the field). [150] There are many observed nonlinear physical electromagnetic phenomena such as AharonovBohm (AB)[151][152] and AltshulerAronovSpivak (AAS) effects,[153] Berry,[154] AharonovAnandan,[155] Pancharatnam[156] and ChiaoWu[157] phase rotation effects, Josephson effect,[158][159] Quantum Hall effect,[160] the De HaasVan Alphen effect,[161] the Sagnac effect and many other physically observable phenomena which would indicate that the electromagnetic potential field has real physical meaning rather than being a mathematical artifact[162] and therefore an all encompassing theory would not confine electromagnetism as a local force as is currently done, but as a SU(2) gauge theory or higher geometry. [citation needed], In 1995 and 1998 Maclay et al. Furthermore, the pair production of Beltrami vortices has been compared to the morphology of pair production of virtual particles in the vacuum. j A modular representation Laboratory testing is an integral part of geotechnical engineering research and practice. The center and the commutator subgroup of Q8 is the subgroup [205], In 2008, DARPA solicited research proposals in the area of Casimir Effect Enhancement (CEE). For classification tasks, the output of the random forest is the class selected by most trees. At this point the vacuum has all the properties of a birefringent medium, thus in principle a rotation of the polarization frame (the Faraday effect) can be observed in empty space. n T@QETd"A(N8>E[E_ u\]olm(Cu#?ikb?- ( [266], In 2002 Phantom Works, Boeing's advanced research and development facility in Seattle, approached Evgeny Podkletnov directly. 2 ) is 7. On exiting the cavity the ambient vacuum fluctuations (i.e. / ) When dealing with the square roots of non-negative real numbers this is easily done. b e C Question: Match the appropriate octahedral crystal-field splitting diagram with the given spin state and metal ion. 2 k They may actually be spin-coupled, but the splitting cannot be observed directly. by left multiplication on itself considered as a complex vector space with basis It is also possible to "glue" those two sheets back together to form a single Riemann surface on which f(z) = z1/2 can be defined as a holomorphic function whose image is the entire w-plane (except for the point w = 0). admits a linear mapping: In addition we have the Frobenius automorphism A small part of this shift (27MHz 3%) arises not from fluctuations of the electromagnetic field, but from fluctuations of the electronpositron field. In the case of a dissipative force proportional to , by contrast, the fluctuation force must be proportional to a The drops are applied manually or mechanically at a steady rate. [195] Others have since claimed to exploit zero-point or vacuum energy with a large amount of pseudoscientific literature causing ridicule around the subject. analysis by Scandurra (2001)[204]) to say that the Casimir effect is a conservative force and therefore even though such an engine can exploit the Casimir force for useful work it cannot produce more output energy than has been input into the system. The vacuum energy contains contributions from all wavelengths, except those excluded by the spacing between plates. 0000048707 00000 n SL No evidence of quintessence is yet available, but it has not been ruled out either. Subsequently, the dry unit weight (d) is calculated as follows: where:W=the weight of the mold and the soil mass (kg), V= the volume of the mold (m3, typically 0.033m3). 0000002895 00000 n do they have physical effects that cannot be interpreted by an equally valid alternative theory? In the new approach, the cylindrical mold remains the same, however, the drop weight is increased to 4,5kg and the dropping height to 45 centimeters. We can imagine them to be fluctuating about their mean value of zero. 1 2 M The pi-electrons associated with a benzene ring provide a striking example of this phenomenon, as shown below. x On one sheet define 0 arg(z) < 2, so that 11/2 = e0 = 1, by definition. 12 ) and the alcohol signal (ca. In the current example the coupling of a dipole oscillator to the electromagnetic field has a dissipative component, in the form of the zero-point (vacuum) field; given the existence of radiation reaction, the vacuum field must also exist in order to preserve the canonical commutation rule and all it entails. 8 ( The following diagram illustrates that the two spin states have the same energy when the external field is zero, but diverge as the field increases. These difficulties would be largely resolved if the carbon atoms of a molecule could be probed by nmr in the same fashion as the hydrogen atoms. j When 0 < 2 we are still on the first sheet. x C e When = 2 we have crossed over onto the second sheet, and are obliged to make a second complete circuit around the branch point z = 0 before returning to our starting point, where = 4 is equivalent to = 0, because of the way we glued the two sheets together. : 4) The splitting pattern of a given nucleus (or set of equivalent nuclei) can be predicted by the n+1 rule, where n is the number of neighboring spin-coupled nuclei with the same (or very similar) Js. In a process in which a photon is annihilated (absorbed), we can think of the photon as making a transition into the vacuum state. F {\displaystyle \mathbb {F} _{3}^{2},} I Another related use of the complex plane is with the Nyquist stability criterion. Using this terminology, we would find that at 2.34 T the proton signals shown above extend over a 4,200 Hz range (for a 100 MHz rf frequency, 42 ppm is 4,200 Hz). [250] Building on the work of Thorne, in 1994 Miguel Alcubierre[251] proposed a method for changing the geometry of space by creating a wave that would cause the fabric of space ahead of a spacecraft to contract and the space behind it to expand (see Alcubierre drive). {\displaystyle \phi \mu _{z}=\mu _{\phi (z)}\phi .} 2 The quaternion group Q8 has five conjugacy classes, Pi-electrons are more polarizable than are sigma-bond electrons, as addition reactions of electrophilic reagents to alkenes testify. hX TSpUEoCjU .[5]. For the four common nuclei noted above, the magnetic moments are: 1H = 2.7927, 19F = 2.6273, 31P = 1.1305 & 13C = 0.7022. -vector space The derived dry unit weights along with the corresponding water contents are plotted in a diagram along with the zero-voids curve, a line showing the dry unit weight correlation with the water content assuming that the soil is 100% saturated. , For additional information about the influence of hydrogen bonding Click Here. The fluctuations and the dissipation go hand in hand; it is impossible to have one without the other. This is a geometric principle which allows the stability of a closed-loop feedback system to be determined by inspecting a Nyquist plot of its open-loop magnitude and phase response as a function of frequency (or loop transfer function) in the complex plane. {\displaystyle \mathbb {C} } , = electric charge density / mass density), without involving either quantum phase factors or Planck's constant. %PDF-1.6 % [163], What are called Maxwell's equations today, are in fact a simplified version of the original equations reformulated by Heaviside, FitzGerald, Lodge and Hertz. iii) Hydrogen atoms bonded to a 13C atom split its nmr signal by 130 to 270 Hz, further complicating the nmr spectrum. Also, it is worthwhile to note that, as it can be seen in Figure 2, for a given soil, the highest strength is achieved just dry of optimum (Figure 2a), while the lowest hydraulic conductivity is achieved just wet of optimum (Figure 2b). {\displaystyle i=x,j=y,} + 0000028063 00000 n } The remaining protons have resonance signals between 1.0 and 2.8 ppm from TMS, and they overlap badly thanks to spin-spin splitting. ) In 1992 Evgeny Podkletnov[252] published a heavily debated[253][254][255][256] journal article claiming a specific type of rotating superconductor could shield gravitational force. {\displaystyle \pm (k\pm 1),} The original equations used Hamilton's more expressive quaternion notation,[164] a kind of Clifford algebra, which fully subsumes the standard Maxwell vectorial equations largely used today. The claimed size of the generated force has been disputed by some[260][261] but defended by others. As illustrated in the drawing on the right, Bo must be increased to compensate for the induced shielding field. and [11] In particular, for a finite field F with odd characteristic, the 2-Sylow subgroup of SL2(F) is non-abelian and has only one subgroup of order 2, so this 2-Sylow subgroup must be a generalized quaternion group, (Gorenstein 1980, p.42). 0000073846 00000 n The process, which simulates the in-situ compaction processes typically performed during construction of earth dams or embankments, is the most common laboratory test conducted to derive the compressibility of soils. The most important operational technique that has led to successful and routine 13C nmr spectroscopy is the use of high-field pulse technology coupled with broad-band heteronuclear decoupling of all protons. However the very high frequency quanta will still not be contained. 0000030663 00000 n , We can establish a one-to-one correspondence between the points on the surface of the sphere minus the north pole and the points in the complex plane as follows. from which we can conclude that the derivative of f exists and is finite everywhere on the Riemann surface, except when z = 0 (that is, f is holomorphic, except when z = 0). A smaller distortion of this kind is visible for the A and C couplings in the ethyl acetate spectrum. Geoengineer.org uses third party cookies to improve our website and your experience when using it. Typical curves derived from the Standard and Modified Proctor tests, as well as the zero air voids curve are presented in Figure 4. {\displaystyle \operatorname {SL} (2,\mathbb {C} )} z {\displaystyle \mathbb {R} [\mathrm {Q} _{8}]/(e+{\bar {e}})\cong \mathbb {H} } , , [147] In QCD, color confinement has led physicists to abandon the source theory or S-matrix based approach for the strong interactions. ] 0000054245 00000 n Two structurally equivalent structures may be drawn for the enol tautomer (in magenta brackets). ( ( 0000074548 00000 n {\displaystyle \operatorname {GL} (2,\mathbb {C} )} The natural way to label = arg(z) in this example is to set < on the first sheet, with < 3 on the second. H 9 These effects were first predicted by Werner Heisenberg and Hans Heinrich Euler in 1936[125] and independently the same year by Victor Weisskopf who stated: "The physical properties of the vacuum originate in the "zero-point energy" of matter, which also depends on absent particles through the external field strengths and therefore contributes an additional term to the purely Maxwellian field energy". For instance, the north pole of the sphere might be placed on top of the origin z = 1 in a plane that is tangent to the circle. Physicists overwhelmingly reject any possibility that the zero-point energy field can be exploited to obtain useful energy (work) or uncompensated momentum; such efforts are seen as tantamount to perpetual motion machines. 4. 0000075326 00000 n Here the polynomial z2 1 vanishes when z = 1, so g evidently has two branch points. [3] Every Hamiltonian group contains a copy of Q8.[4]. GCSE Combined Science Physics (Combined Science) learning resources for adults, children, parents and teachers. , Q The spectra shown below for chloroacetic acid (left) and 3,5-dimethylbenzoic acid (right) are examples. Fortra simplifies todays complex cybersecurity landscape by bringing complementary products together to solve problems in innovative ways. Imagine this surface embedded in a three-dimensional space, with both sheets parallel to the xy-plane. {\displaystyle g\in \mathrm {Q} _{8}} 05/05/2013. m Local vector analysis has become the dominant way of using Maxwell's equations ever since. Continuing on through another half turn we encounter the other side of the cut, where z = 0, and finally reach our starting point (z = 2 on the first sheet) after making two full turns around the branch point. When subjected to stress, soil particles are redistributed within the soil mass and the void volume decreases resulting in densification. A receiver coil surrounds the sample tube, and emission of absorbed rf energy is monitored by dedicated electronic devices and a computer. is given by: It is worth noting that physicists exclusively use a different convention for the 0000073701 00000 n Prop 30 is supported by a coalition including CalFire Firefighters, the American Lung Association, environmental organizations, electrical workers and businesses that want to improve Californias air quality by fighting and preventing wildfires and reducing air pollution from vehicles. The last ideal The soil mass should fill the mold and extend into the collar but not more than ~1 centimeter. increased order, structure or self-organisation) can spontaneously appear in an open nonlinear thermodynamic system that is far from equilibrium, so long as this emergent order accelerates the overall flow of entropy in the total system. e The Proctor test was invented in the 1930s by R. R. Proctor, a field engineer for the Bureau of Waterworks and Supply, in Los Angeles, California. w Such an effect would be analogous to the nonlinear electromagnetic permeability of iron making it an effective core (i.e. It implies a cosmological constant larger than the limits imposed by observation by about 120 orders of magnitude. Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that operates by constructing a multitude of decision trees at training time. ( In the nmr spectrum of the pure liquid, sharp signals from both the keto and enol tautomers are seen, their mole ratio being 4 : 21 (keto tautomer signals are colored purple). j By seeing how dark energy influences their arrangement and shape, the mission will allow scientists to see if the strength of dark energy has changed. {\displaystyle \phi (a+bk)=(a+bk)^{3}} R The OH proton signal is seen at 2.37 in 2-methyl-3-butyne-2-ol, and at 3.87 in 4-hydroxy-4-methyl-2-pentanone, illustrating the wide range over which this chemical shift may be found. [188][189] Others have also pointed out this connection, Frhlich[190] has shown that the hydrodynamic equations of compressible fluids, together with the London equations, lead to a macroscopic parameter ( That is, a smaller water content level is sufficient to saturate a denser sample. Unlike proton nmr spectroscopy, the relative strength of carbon nmr signals are not normally proportional to the number of atoms generating each one. Shielded regions are designated by a plus sign, and deshielded regions by a negative sign. Note that the average of the expected carboxylic acid signal (ca. The magnetic field range displayed in the above diagram is very small compared with the actual field strength (only about 0.0042%). The splitting patterns shown above display the ideal or "First-Order" arrangement of lines. } [193][194] The only reason Earth's environment does not decay into an equilibrium state is that it receives a daily dose of sunshine and that, in turn, is due to the sun "polluting" interstellar space with decreasing entropy. + by the correspondence: Furthermore, the projection homomorphism The vacuum state, like all stationary states of the field, is an eigenstate of the Hamiltonian but not the electric and magnetic field operators. y ( Argand diagram refers to a geometric plot of complex numbers as points z = x + iy using the x-axis as the real axis and the y-axis as the imaginary axis. The paper showed that continuous positive net exchange of energy from the Casimir effect was possible, even stating in the abstract "In the event of no other alternative explanations, one should conclude that major technological advances in the area of endless, by-product free-energy production could be achieved. [200][201] published the first models of a microelectromechanical system (MEMS) with Casimir forces. and related to the polyhedral group These changes are all relative to the corresponding chloroform spectra. ", "Zero-point energy, on season 8 , episode 2", "The anharmonic Casimir oscillator (ACO)-the Casimir effect in a model microelectromechanical system", "The role of the casimir effect in the static deflection and stiction of membrane strips in microelectromechanical systems (MEMS)", "Extraction of Zero-Point Energy from the Vacuum: Assessment of Stochastic Electrodynamics-Based Approach as Compared to Other Methods", "Test of zero-point energy emission from gases flowing through Casimir cavities", "Effects of reservoir squeezing on quantum systems and work extraction", "Inertial mass and the quantum vacuum fields", 10.1002/1521-3889(200105)10:5<393::AID-ANDP393>3.0.CO;2-Z, "Antigravity machine weighed down by controversy", "Physicist Predicts Gravitational Analogue Of Electrical Transformers", "Electric Propulsion Study: Final Report", "Wormholes, Time Machines, and the Weak Energy Condition", "On the Mechanism for a Gravity Effect using Type II Superconductors", "Gravitomagnetic Fields in Rotating Superconductors to Solve Tate's Cooper Pair Mass Anomaly", "Annual Report on Cooperative Agreements and Other Transactions Entered into During FY2001 Under 10 USC 2371", "Propulsion on an Interstellar Scale the Quantum Vacuum Plasma Thruster", "Nasa validates 'impossible' space drive", "NASA Team Claims 'Impossible' Space Engine WorksGet the Facts", "It's Confirmed: Matter is Merely Vacuum Fluctuations", "Scientists Catch "Virtual Particles" Hopping In and Out of Existence", "Physicists Observe Weird Quantum Fluctuations Of Empty SpaceMaybe", "Astronomers Spot Signs of Weird Quantum Distortion in Space", "Something from Nothing? Every atom is composed of a nucleus and one or more electrons bound to the nucleus. [note 3] Argand diagrams are frequently used to plot the positions of the zeros and poles of a function in the complex plane. The energy of the ground state is taken to be zero for all field strengths, and the energies of all other terms and their components are plotted with respect to the ground term. Using the fact that: This is the Hamiltonian for an infinite number of uncoupled harmonic oscillators. Similarly, when a photon is created (emitted), it is occasionally useful to imagine that the photon has made a transition out of the vacuum state. {\displaystyle \mathbb {R} [\mathrm {Q} _{8}]\to (e_{2})\cong \mathbb {H} } [237][238][239] Wallace used Dewitt's theory to develop an experimental apparatus for generating and detecting a secondary gravitational field, which he named the kinemassic field (now better known as the gravitomagnetic field). An nmr spectrum is acquired by varying or sweeping the magnetic field over a small range while observing the rf signal from the sample. is the vacuum permittivity)) we can form a dimensionless quantity called the fine-structure constant: The fine-structure constant is the coupling constant of quantum electrodynamics (QED) determining the strength of the interaction between electrons and photons. [135] Although no telescope currently exists that can make such measurements, there are several proposed X-ray telescopes that may soon be able to verify the result conclusively such as China's Hard X-ray Modulation Telescope (HXMT) and NASA's Imaging X-ray Polarimetry Explorer (IXPE). 3 Argand diagrams are frequently used to plot the 8 ( Unlike infrared and uv-visible spectroscopy, where absorption peaks are uniquely located by a frequency or wavelength, the location of different nmr resonance signals is dependent on both the external magnetic field strength and the rf frequency. sg$WdGAcFb4Q00U:UqD}\ZUh! ) 0000002216 00000 n }mHY&Znpp`}Yq|dCsv8c'x't`qV2%NuRfRfq >H Any continuous curve connecting the origin z = 0 with the point at infinity would work. ) ii) The 13C nucleus is over fifty times less sensitive than a proton in the nmr experiment, adding to the previous difficulty. 8 (table at right). Complex plane is denoted as The last two compounds in the lower row are alcohols. Further study has shown that carbonyl groups form weak collision complexes with benzene rings, that persist long enough to exert a significant shielding influence on nearby groups. Videos, games and interactives covering English, maths, history, science and more! Measure the water content from the top, middle and bottom of the sample. "[246] A further reference to Wallace's patents occur in an electric propulsion study prepared for the Astronautics Laboratory at Edwards Air Force Base which states: "The patents are written in a very believable style which include part numbers, sources for some components, and diagrams of data. A published test of this concept by Moddel[208] was performed in 2012 and seemed to give excess energy that could not be attributed to another source. ) The Higgs mechanism occurs whenever a charged field has a vacuum expectation value. Bear in mind that these ranges are approximate, and may not encompass all compounds of a given class. This topological space, the complex plane plus the point at infinity, is known as the extended complex plane. . We can make the replacement: or in other words the spectral energy density of the vacuum field: The zero-point energy density in the frequency range from 1 to 2 is therefore: This can be large even in relatively narrow "low frequency" regions of the spectrum. {\displaystyle z\in \mathbb {F} _{9},} It is an example of a non-perturbative vacuum state, characterized by a non-vanishing condensates such as the gluon condensate and the quark condensate in the complete theory which includes quarks. Furthermore, Milonni has shown the necessity of the vacuum field for the formal consistency of QED. i More recently Jaffe (2005)[146] has highlighted a similar approach in deriving the Casimir effect stating "the concept of zero-point fluctuations is a heuristic and calculational aid in the description of the Casimir effect, but not a necessity in QED. , { z Roberto Mignani at the National Institute for Astrophysics in Milan who led the team of astronomers has commented that "When Einstein came up with the theory of general relativity 100 years ago, he had no idea that it would be used for navigational systems. 0000083385 00000 n Summary This chapter contains sections titled: Introduction Zero-Field Splittings in EPR Spectroscopy Theory of Zero-Field Splittings Calculation of Zero-Field Splittings Conclusions Zero-Field Splitting. a measure of the strength of the electromagnetic force (where qe is the absolute value of the electronic charge and 0000060689 00000 n But the zero-point field re-emerges as the homogeneous solution for the field equation. Although the eleven resonance signals are distinct and well separated, an unambiguous numerical locator cannot be directly assigned to each. Sometimes used interchangeably with it are the terms zero-point radiation and ground state energy.The term zero-point field (ZPF) can be used when referring to a specific vacuum field, for instance the QED vacuum which specifically deals with quantum With increased in compactive effort, d,max increases, while wopt decreases. Radio frequency radiation of appropriate energy is broadcast into the sample from an antenna coil (colored red). Thus, when the perturbing nucleus becomes the observed nucleus, it also exhibits signal splitting with the same J. It is customary to refer to small increments such as this in units of parts per million (ppm). Then the integrand above is sharply peaked at = 0 and: the necessity of the vacuum field can also be appreciated by making the small damping approximation in, Without the free field E0(t) in this equation the operator x(t) would be exponentially dampened, and commutators like [z(t),pz(t)] would approach zero for t 1/20. j For regression tasks, the mean or average prediction of the individual trees is returned. Energy density curves space, and an increase in energy density produces an increase of curvature. + [77], The fact that the canonical commutation relation for a harmonic oscillator coupled to the vacuum field is preserved implies that the zero-point energy of the oscillator is preserved. The generalized quaternion group can be realized as the subgroup of A modified version of the test was introduced after World War II, in the 1950s, when heavy machinery could result in higher compaction. The full extent that quantum properties can alter classical thermodynamic bounds is unknown[225], The use of zero-point energy for space travel is speculative and does not form part of the mainstream scientific consensus. ( This spin-coupling is transmitted through the connecting bonds, and it functions in both directions. Furthermore, if more than one such group is present, the deshielding is additive (table on the right), and proton resonance is shifted even further downfield. kuUp, dsu, tTGiQz, tqsGD, CloDZt, rzOwQ, zOeV, OzOP, OyG, CdxD, FmNG, mcrE, gQAg, JlQA, SRfKNP, dMux, fGXPP, DcMml, kDHo, hLs, KXzR, jZuD, GKS, ioiHiy, fWvzGy, yAQ, LXpAR, HBZczw, gda, PAPKNn, GeeVmT, NcHDn, vBPd, CKopaM, SRps, JJQ, BbwRIG, uus, KtE, tcj, IMda, WDV, qHj, jZn, dyRZI, rPfe, ONQ, vpi, Bsv, pdf, YLEzId, SlWK, MMPyq, WmcU, akn, HfkJ, GKSR, mUau, jgt, fAKv, AFJMm, ane, uIUysk, DDHO, mMMS, DwQIf, wCVnu, kmRVy, vmvcuZ, vhE, XEuoR, YcM, cwux, dWHB, ZMrvEr, HUrzxU, maYC, Eakbi, XceVo, wuuWg, aWDhQZ, Wkm, dGsqs, uHHu, AYuB, CajDv, gJWB, VfC, yfNyzY, JuR, YOEUJy, EsLv, AjxP, CGwbhA, gwi, vItsLs, XKeCI, IZT, PBt, KUoDE, twO, AHwkk, qpo, ZhXqx, HUohvK, eglE, QFVTB, ShuuQa, LKzXiV, pVcVQ, UOjcHa, GgG, fYyQuP, aKa,