Pj Problems - Overview
The Number Line
7 Spaces Of Interest - Overview
Triadic Unit Mesh
States Of Matter
COHN - Natures Engineering Of The Human Body
The Human-Body Systems
Faith, Love, Charity
Timely information (particularly in living organisms) is an existential demand. So, there exist existential information supply chains.
(a) What is information?
(bi) In what primary forms is information transmitted in the human body?
(ii) Identify the information supply chains in the human body.
(iii) Indicate the PjProblemStrings Sequences of the information supply chains.
(iv) Which of the 7 types of PjProblemStrings Sequences are present in the information supply chains in the human body?
(ci) How has the human body secured its information supply chains?
(ii) Is the security perfect?
(iii) What lessons can humans learn from how information supply chains are secured in the human body?
(di) Name some important hormones, the information they contain and the glands that secrete them in the human body.
(ii) Name the organs that receive the hormonal information named in (di) and describe how they respond to the information
(e) Briefly state the fundamental biologic cycle of information.
(fi) How is the information supply chains of the human body similar to the information supply chains called the internet.
(fii) How is the information supply chains of the human body dissimilar to the information supply chains called the internet.
S7P3A3k (force -k =1, 2), S7P4A4k (motion- k =1, 2, 3,4).
All Pj Problems are at play. However, Pj Problems of Interest are of types force and motion.
(a) Information is shared knowledge. Knowledge is the product of stimuli-processing (the brain is the stimuli-processor in humans). In other words, knowledge is the understanding established by cognitive beings as a result of their processing of the interactions between their senses and their environments. Knowledge may or may not be factual. So, information may or may not be factual. Data is knowledge obtained from the scientific method. Nature, as original owner of Knowledge, initialized information when it first shared its knowledge with cognitive beings. So, the Human Knowledge-Information Continuum is continually being populated by the knowledge shared between Nature and humans; between humans; between humans and other cognitive beings; and between other cognitive beings (in modern times, some machines have become cognitive). Information can be shared. In this case, the sharer of information is not the original owner of the knowledge being shared. In other words, the sharing of information implies that the original knowledge has been shared at least once by the original owner of the knowledge being shared.
Communication is the transmission of Information between cognitive beings through a medium or media.
(bi) Information is transmitted in the human body in the form of electrical impulses, and chemicals (e.g. hormones).
(bii) The information supply chains in the human body can be broadly grouped into:
- External supply chains: information originates from outside the body.
- Internal supply chains: information originates from inside the body.
Then subgrouped according to distance travelled by the information:
-- Autocrine signaling (cell signals itself).
-- Paracrine signaling (signaling between cells in the same tissue or organ).
-- Endocrine signaling (gland to gland/organ signaling).
-- Neuroendrocrine signaling (nervous system signals the endorine system).
-- Neurocrine signaling (signaling within the nervous system).
-- Juxtacrine signaling (signaling between adjacent cells).
External Supply Chains
Supply Chain: sensory organs systems (e.g. eye, ear, nose, tongue, skin)
Signals (sensory input) supplied to sensory organs: stimuli (e.g. light, sound, smell, taste, touch).
Signals supplied by the sensory organs: stimuli (e.g. charge differential).
Supply Chain: the nervous system.
Signals supplied to the nervous system: stimuli (e.g. charge differential).
Signals supplied by the nervous system: electrical impulses and neurotransmitters.
The neurons (nerve cells) transport the signals. The dendrites of a neuron receive the signal, the axon transmits the signal to the terminal of the neuron, neurotransmitters in the synapses (gaps between neurons) transmit the signal to the next neuron.
Internal Supply Chains
Supply Chain: the endocrine system
materials supplied to endocrine system: hormones.
Materials supplied by the endocrine system: hormones.
Supply Chain: neuroendocrine integration
signals supplied to glands: neurotransmitters.
Materials supplied by the glands: hormones
Supply Chain: non-glandular organs (liver, kidney, stomach)
signals supplied to non-glandular organs: stimuli (e.g. concentration differential).
Materials supplied by non-glandular organs : hormones
The blood transports the hormones secreted by the endocrine system.
Supply Chain: protein synthesis
material supplied for protein synthesis: genes
Material supplied by protein synthesis: proteins
Messenger Ribonucleic acid (mRNA) transports the codons that specify the particular amino acids used for protein synthesis.
PjProblemStrings Sequences of Supply Chains
A PjProblemString Sequence is a sequence of PjProblemStrings (SiPjAjk: a space of interest stringed to a particular problem of interest, k not a multiplicand). Supply chains are configurations of PjProblemStrings Sequences. The PjProblemString Sequences that are of primary importance are:
SiP2A2kSiP6A6k - Identification and grouping of contents in space of interest.
SiP3A3kSiP4A4kSiP3A3k - Analysis of the dynamics of the space of interest. This involves motion sandwiched between two forces . The first force is the active force and the second is resistive force. The difference between the active force and the resistive force is the resultant force (driving force) causing the motion. In some scenarios, the active force is deliberately reduced in order to reduce or stop the motion (e.g. a runner reduces speed after crossing the finishing line). When the resultant force is zero, there is static equilibrium. When the resultant force is constant, there is dynamic equilibrium. The PjproblemStrings of change are implicit in the dynamism.
primary sources of forces in the human body
Muscles (skeletal, smooth and cardiac), hydrostatic pressure, vascular elasticity, enzyme actions, attractive and repulsive forces of atoms, electrochemical gradients are the primary sources of forces in the human body.
(biii) Supply chain: the eye as a sensory organ
The eye is the sense organ of sight. The eye is a three-layered ball-like shape with a frontal bulge.
- The outer layer is the sclera (the white of the eye) and the bulge of the sclera in front of the eye is the cornea.
- The middle layer is the choriod. It contains the iris (the colored part of the eye). In the center of the iris is an opening called the pupil. The lens is behind the iris.
- The inner layer is the retina. It consists of the sensory retina that contains the nerve cells and the retinal pigment epithelium (RPE) which lies between the sensory retina and the wall of the eye.
The space between the cornea and the iris is called the anterior chamber.
The space between the iris and the lens is called the posterior chamber.
The space between the lens and the back of the eye is called the vitreous chamber. Two-thirds of the inner wall of the vitreous chamber contains the retina.
The eye contains two types of fluids: the aqueous humor (clear and watery) in both the anterior and posterior chambers; and the vitreous humor (thick and gel-like) in the vitreous chamber. The pressures of the fluids on the inside of the eyeball help the eye maintain its shape.
PjProblemStrings Sequences Of The Eye As A Supply Chain
Important relevant statements:
- A photon (light particle) goes from place to place.
- An electron goes from place to place.
- An electron emits or absorbs a photon.
Motion sandwiched: movement of light from luminous object (object that produces and emits light) to illuminated object (object that reflects light).
Forces sandwiching motion: heat energy and electromagnetic force.
The emission of photons by electrons is a consequence of electron excitation. Electrons are excited when they absorb energy. Then the excited electrons jump to higher energy levels. The higher energy level is not as stable as their previous lower energy level so they emit the absorbed energy in the form of photons. Then they are pulled back to their more stable lower energy level by the electromagnetic force of the atom's nucleus.
Motion sandwiched: movement of light from illuminated object to retina of eye.
Forces sandwiching motion: pigement actions and muscle actions.
Pigments are substances that selectively absorb visible light of certain wavelengths and thus have charactristic colors. All objects have pigments. The light not absorbed by the pigments of an object is reflected. So, the reflected light from an illuminated object that reaches the eye is the light not absorbed by the pigments of the illuminated object.
Assuming a healthy eye, reflected light gets to the retina: lens muscles provide the elasticity the lens needs to change its shape so that it can focus on objects at varing distances (near or far objects); The muscles of the iris closes (constrict) or opens (dilate) the pupil to control the amount of light that enters the eye; the cornea, aqueous humor, lens and vitreous humor refract the light to the retina.
Muscles of the eyelids may close the eyelids to prevent the light from entering the eye.
Motion sandwiched: movement of light from retina to nerve cell.
Forces sandwiching motion: light energy and potential difference.
The retina is lined with two types of photoreceptors: rods (about 120 millions) and cones (about 7 millions). Rods are for monochrome vision. Cones are for color vision.
In a section at the tops of a rod and a cone are membrane-bound discs. These discs contain proteins bound to chromophore 11-cis-retinal (a chromophore is a molecule with a typical color as a result of its ability to absorb light of a specific wavelength).
The protein which bind the chromophore 11-cis-retinal in rod cells is opsin. This complex (i.e. 11-cis-retinal and opsin together) is called rhodopsin.
Rhodopsin of a rod cell absorbs light and is isomerized. Consequently, 11-cis-retinal in rhodopsin changes structurally to all-trans-retinal. The resulting complex is called bathorhodopsin (fig 1). The elongated shape and rigidity of the all-trans-retinal causes it to be unstable within the protein and its eventually expelled at the completion of a series of conformational changes associated with the cis-trans isomerization. The intermediates before all-trans is set free are as follows:
The intermediate necessary for vision is metarhodopsin II. It activates the enzyme transducin which begins the signal transduction cascade that results in the electical impluse that the nerve cell sends to the brain for interpretation. The free trans-retinal undergoes a multiple step conformational changes that regenerates 11-cis-retinal.
The vision process in cones is slightly differenct from that in rods because cones are responsible for trichromatic color vision. Consequently, there are three photoreceptors in cones: red-absorbing, green-absorbing, and blue-absorbing cone cells. Each photoreceptor represents one of the three primary colors (red, green and blue) and each type also has a different protein that bind to 11-cis-retinal. The proteins are different from rhodopsin because the sequence of amino acids at the location where the proteins bind to retinal are different from the amino sequence at similar location in rhodopsin. Their absorbance characteristics are also different.
PjProblemStrings Sequences Of The Nervous System As Supply Chain
The nervous system consists of the Central Nervous System (distribution of nerve cells in the brain and spinal cord); and the Peripheral Nervous System (distribution of nerve cells from the spinal cord to other parts of the body).
The Peripheral Nervous System consists of the Somatic Nervous System which controls voluntary movements such as walking; and the Autonomic Nervous System which controls involuntary movements such as the cardiac circle, breathing, digestion.
The Human Brain
The human brain is a 3 lb organ cushioned by the cerebrospinal fluid (fluid inside and around the brain) and protected by the skull (a sutured fusion of eight bones).
Neurons: nerve cells that make up the brain and the rest of the nervous system. Broadly grouped into:
- Sensory neurons (receive signals from stimuli and transmit the information to the brain or spinal cord)
- Interneurons (relay brain's response to motor neurons)
- Motor Neurons (relay information to muscles and glands for action)
Areas of the central nervous system where neuronal soma (cell body of neurons) are found are called gray matter.
Areas of the central nervous system where axons are found are called white matter.
Glia cells: provide neurons with nourishment, protection and structural support. They are more numerous than the neurons (there are about 10 to 50 times more glia cells than neurons). Broadly grouped into:
- Astroglia or Astrocytes: these glia cells are the official protectors of neurons. They ensure proper interactions between neurons and nutrients and other molecules, by regulating the blood-brain barrier. They control homeostasis, repair neurons and influence electrical impulses.
- Oligodendroglia cell: they are the producer of myelin, the fatty substance that insulate axons. Myelin sheath around axons enable quick travel of electtrical impulses.
-Ependymal cells: these cells line the ventricles (hollow fluid-filled cavities in the brain) and are the producers of the cerebrospinal fluid.
Microglia: these are the immune cells of the brain. They stand guard and destroy invaders, clean up messes left around and prune synapses.
Meninges (three-layered tissues that protect the brain):
- The Dura mater (thick outerlayer that lines the inside of the skull)
- The Arachnoid mater (weblike, elastic, thin middlelayer that covers the entire brain).
- The Pia mater (innerlayer that directly covers the surface of the brain following the folds and the groves).
- The Pia mater is rich in blood supply that reaches deep inside the brain.
- The Subarachnoid is the space between the Arachnoid mater and the Pia mater that contains the cerebrospinal fluid.
Three main divisions of the brain:
Cerebrum: is the largest part of the brain. It is divided into two hemispheres: the left hemisphere which controls the right side of the body and is generally responsible for language and speech; and the right hemisphere which controls the left side of the body and is generally responsible for visual and spatial interpretation. The surface of the cerebrum is called the cortex.
- Each hemisphere is sectionalized into 4 lobes within which are sections with specific functions:
-- The Frontal Lobe is responsible for:
--- Pesonality, behaviour and emotions
--- Judgement, planning, and problem solving
--- Intelligence, concentration and self-awareness
--- Contains the Broca's area, the subsection responsible for speaking and writing
--- Contains the Motor Strip, the subsection responsible for body movement.
-- The Parietal Lobe is responsible for:
--- Spatial and visual perception
--- Language, words
--- Interpreting signals from vision, hearing, motor, sensory and memory
--- Contains the sensory strip, the subsection responsible for the sense of touch, temperature and pain.
-- The Occipital Lobe is responsible for:
---interpreting the color, light and movement inherent in vision.
-- The Temporal Lobe is responsible for:
--- Sequencing and organization
--- Contains the Wernicke's area, the subsection responsible for understanding language
Inter lobes and inter hemispheres communications and cooperations are the normal relationships of the parts of the cerebrum.
Cerebellum: is located under the cerebrum and is responsible for the coordination of muscle movements, maintenance of posture and balance.
Brain Stem: connects the cerebrum and the cerebellum to the spinal chord acting as a relay center. It is responsible for many of the body's automatic functions such as the heart rate, breathing, digestion, the circadian circle (wake and sleep circle), body temperature, sneezing, coughing, swallowing, vomiting, etc.
The skull in addition to being protective of the brain, offers exit holes (foramina) at the three major areas (anterior fossa, middle fossa and posterior fossa) of the base of the skull, for arteries, veins and nerves. The foramen magnus is where the brain stem exits the skull.
Twelve pairs of cranial nerves constitute communication conduits by which the brain communicates with some part of the body as described in the diagram. The brain's other communication conduit is the spinal cord.
The first and second (I II) nerves (olfactory and optic) originate from the cerebrum. The remaining ten nerves (II, IV, V, VI, VII, VIII, IX, X, XI,XII), originate from the brain stem.
The Spinal Cord
The spinal cord (about 18 inches long) is a tubular nerve tissue covered by the three layered meninges (Dura mater, Arachnoid mater and Pia mater). Like the brain, the cerebrospinal fluid is contained in the subarachnoid space (the space between the Arachnoid mater and Pia mater). The spinal cord begins at the medulla oblongata of the brain stem; exits through the foramen magnum into a central canal (the spinal canal) inside a column of protective bones called the vertebrae; and ends between the first and second lumbar vertebrae. A bundle of nerves called the cauda equina is attached to the end of the spinal cord and extends into the coccyx (the last bone structure of the vertebral column).
The Vertebrae: the column of bones that protect and support the spinal cord. It is grouped into 5 regions: the cervical vertebrae (there are 7); the thoracic vertebrae (there are 12); the lumbar vertebrae (there are 5); the sacrum (there is 1); the coccyx (there is 1). A layer of cartilage (disk) rest between the vertebrae to provide cushioning.
The primary functions of the spinal cord are to relay:
- Information (sensory or afferent signals) from the body to the brain
- Information (motor or efferent signals) from the brain to the body.
- spinal cord response to some sensory input autonomously (e.g. reflexes) through the reflex arc without the brain's participation.
A spinal nerve is a combination of a posterior sensory root and an anterior motor root. The sensory root emerges from the back (posterior) of the spinal cord through the sensory root pathway while the anterior motor root emerges from the front (anterior) through the motor root pathway (see diagram).
31 left-right pairs of spinal nerves relay the sensory (afferent) and motor (efferent) signals to and from the brain. The first pair emerge from the opening between the occipital bone and the first vertebra (the atlas). The remaining 30 pairs emerge pair by pair from the intervertebral openings called the intervertebral foramina (an opening is a foramen). In general, spinal nerve refers to a mixed sensory, motor and autonomic nerves that carry signals between the spinal cord and the body.
Spinal nerves are named according to the region of the spinal column from which they emerge:
- Cervical Spinal Nerves: there are 8 (C1-C8). There is no eighth cervical vertebra, however there is an eighth cervical spinal nerve.
- Thoracic Spinal Nerves: there are 12 (T1-T12).
- Lumbar Spinal Nerves: there are 5 (L1-L5).
- Sacral Spinal Nerves: there are 5 (S1-S5).
- Coccygeal Spinal Nerves: there is one
Spinal nerves branch into four primary groups as they emerge from the spinal cord:
- Anterior group (also called the ventral ramus or rami): this group of spinal nerves innervate the anterior trunk (ventral trunk) through the ventrolateral surface.
- Posterior group (also called the dorsal ramus or rami): this group of spinal nerves provide visceral motor, somatic motor and sensory innervations for the dorsal trunk (skin and back muscles).
- Meningeal group: this group innervate the vertebrae themselves and the surrounding structure of the spinal column (the dura, ligaments, blood vessels, intervetebral disks, facet joints, and periosteum.
- Rami communicantes: this group contain the autonomous nerves that transport visceral motor and sensory information to and from the visceral organs.
The branching of spinal nerves into groups is not entirely orderly. Some branchings involve the intersection of branches. A branching network of intersecting nerves that serve the same part of the body is called a nerve plexus. There are six primary nerve plexuses:
- Cervical Plexus: consists of the cutaneous (skin) and muscular branches; belongs to the anterior group (ventral rami). Consists of the first four cervical spinal nerve (C1 to C4). They innervate the back of the head and some neck muscles.
- Brachial Plexus: consists of several subdivisions including the cutaneous (skin) and muscular branches. Consists of the lower four cervical nerve roots (C5 to C8) and the first thoracic nerve root (T1). They innervate the armpit (axilla), arm (brachium), forearm (antebrachium) and hand.
- Lumbar Plexus: formed from the anterior division of the first four lumbar nerves (L1 to L4) and the last thoracic nerve (T12) called the subcostal nerve. They innervate the lower abdominal wall, the thigh, external genitals. The large femoral nerve that innervates the anterior muscles of the thigh is part of this plexus.
- Sacral Plexus: formed by the anterior division of the first sacral nerve (S1), part of the anterior division of the second and third sacral nerves (S2, S3). Lumbar Plexus and the Sacral Plexus are sometimes grouped as the Lumbosacral Plexus. The Lumbosacral thrunk joins both plexuses. The sacral plexus innervate the posterior thigh, most of the lower leg, the entire foot, and part of the pelvis. The sciatic nerve (largest and longest nerve in the human body) is part of the sacral plexus.
- Coccygeal Plexus: formed by the fourth sacral nerve (S4), the fifth sacral neve (S5), and the first coccogeal spinal nerve (Co1). The coccygeal plexus connects to the lower end of the sacral plexus. The anococcygeal nerve is the only nerve in the plexus. It provides sensory innervation to the skin in the coccygeal region.
- Autonomic Plexuses: includes the Celiac Plexus (innervates internal organs), Auerbach's Plexus (innervates the gastrointestinal tract), and Meissner's Plexus (also called the submucosal plexus, innervates the gastrointestinal tract).
PjProblemStrings Sequences Of Neural Supply Chain
Important relevant statements:
- Neurons (nerve cells) form the information network in the human body
- Interacting neurons are separated by gaps called synapses
- A neuron can be a presynaptic neuron or postsynaptic neuron depending on whether or not it is sending or receiving information. The neuron sending information is a presynaptic neuron. The neuron receiving the information is a postsynaptic neuron
- Neurotransmitters are the messengers between neurons. A neurotransmitter is a chemical secreted into the synapse by the presynaptic neuron, travels across the synapse and is received by receptors in the postsynaptic neuron
- neurotransmitters can be either excitatory (help in the transmission of information) or inhibitory (block the transmission of (information).
Motion sandwiched: motion of electrical signals through the presynaptic neuron to the synapse.
Forces sandwiching motion: potential difference.
The depolarization of the resting potential at the semi-permeable membrane (a phospholipid bilayer with hydrophobic core) of neurons powers the transmission of electrical signals to the synapse. This power is called the action potential. Repolarization stops the transmission.
The potential across the semi-permeable membrane of a neuron at rest (not sending signals) is called its resting potential and is established as a result of control of ion-influx into the cell. For example, at rest, potassium ions (K+) cross membrane easily but sodium ions (Na+) and chlorine ions (Cl-) do not cross easily and negatively charged protein molecules inside neuron are disallowed from crossing the membrane. At rest, there are more K+ ions inside the cell and more Na+ ions outside the cell.
The distribution of ions within the cell (cytosol) and outside the cell (extracellular fluid) establishes the resting potential of -70mV (millVolts).
Depolarization is the process of reducing the negatively charged environment of the cytosol to 0mV. In order to initiate depolarization, at least one channel must open to allow the influx of cations (specifically Na+). There are several such channels that respond to varied stimuli. For example, the ligand-gated Na+ channel opens when a neurotransmitter binds to it; the mechanically gated Na+ opens when a physical stimulus activates a sensory receptor (e.g. pressure on the touch receptor); and a voltage gated Na+ channel responds to potential difference. Once a voltage gated Na+ activation channel is opened as a response to stimulus, Na+ starts to enter the cell and the cell begins to become less negative.
Action potential is triggered when the cell is depolarized from -70mV to -55mV. The -55mV is the threshold voltage. This means that the cell will not send electrical signals if depolarization does not attain -55mV. Furthermore, depolarizing beyond -55mV does not magnify the action potential. In essence, the occurence of action potential is a binary event. It either occurs when depolarization reaches -55mV; or it does not occur.
Action potential starts at the initial segment of the axon (the beginning of the axon next to the cell body). The manner it propagates depends on whether or not the axon is myelinated or unmyelinated.
In unmyelinated axon propagation, action potential propagation is sustained because the Na+ that flow into the cell when a voltage gated Na+ channel opens, moves along the inside of the cell membrane. This movement causes the depolarization of adjacent regions which causes the opening of voltage gated Na+ channels which causes the influx of Na+ that move along the inside of the cell membrane. The sequence continues to the axon terminal. Unmyelinated axon propagation is called continuous conduction.
In myelinated axon propagation, action potential is sustained by fewer voltage gated Na+ channels at Nodes of Ranvier. The nodes are optimally placed so that action potential is sustained between nodes. Fewer voltage gated Na+ channels along the axon allow faster transmission of electrical signal. The diameter of the axon also influences the speed of transmission (flow resistance is lower in wider axons). Myelinated axon propagation is called Saltatory (leaping) conduction.
Action potential peaks at about +30mV. However, repolarization is activated about -50mV because this is the voltage that sensitizes the voltage gated K+ channel. The voltage gated K+ channel slowing opens at about the time the Na+ influx into the cell is peaking and the voltage gated Na+ activation channel is being closed. By the time the action potential attains its peak, the voltage gated K+ channel has been fully opened to allow sufficient outflow of K+ to cause repolarization and a hyperpolarization overshoot (polarizing the inside of the cell beyond -70mV). After the repolarization phase, the Na+-K+ pump and the leakage channel (opens and closes at random) normalize the distribution of ions in order to establish the resting potential.
Motion sandwiched: neurotransmitter discharge into synaptic cleft.
Forces sandwiching motion: concentration gradient of calcium ions (Ca2+).
Neurotransmitters are produced in the cell body of the neuron and transported to the axon terminal where they are stored in vesicles (membrane-bound spheres filled with neurotransmitters). Voltage gated calcium ions channel is activated when action potential arrives at the axon terminal. The concentration gradient of Ca2+ (concentration of Ca2+ higher outside the cell than inside the cell) causes an influx of Ca2+ into the cell. The Ca2+ allow the vesicles to fuse with the axon terminal membrane from where the neurotransmitters are discharged into the synaptic cleft (the small gap between the axon terminal of the presynaptic neuron and the membrane of the postsynaptic neuron).
Motion sandwiched: motion of neurotransmitters across synaptic cleft
Forces sandwiching motion: diffusion
The neurotransmitters get to the the postsynaptic neuron membrane by diffusion. This motion can be impeded by:
- difussion: neurotramsmitters drift away from the postsynaptic neuron such that they are no longer able to bind to their receptors.
- Reuptake: neurotransmitters are taken back by the axon terminal.
- Glial cells: neurotransmitters are removed from the synaptic cleft by astrocytes.
- Enzyme action: structure of neurotransmitter is changed by a specific enzyme. Consequently, neurotransmitter is unrecognized by its receptor.
Motion sandwiched: reception of neurotransmitters by receptors of postsynaptic neuron
Forces sandwiching motion: protein receptor action
The neurotransmitters' arrival at the postsynaptic neuron's membrane activates the ligand gated ion channels (a ligand is a signal molecule that binds to a specific receptor) and the neurotransmitter bind to their protein receptors. Consequently, ion channels are opened or closed in the cell membrane and the cell is either depolarized (excited) or hyperpolarized (inhibited). In non-ion channel receptor binding, the receptor activates ion channels through a signal transduction mechanism (set of cell changes induced by receptor activation).
PjProblemStrings Sequences Of The Endocrine System As Supply Chain
To Be Continued.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring
Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle
Derivation Of The Area Of An Ellipse
Derivation Of Volume Of A Cylinder
Derivation Of Volume Of A Sphere
Derivation Of Volume Of A Cone
Derivation Of Volume Of A Torus
Derivation Of Volume Of A Paraboloid
Volume Obtained By Revolving The Curve y = x2 About The X Axis
Single Variable Functions
Absolute Value Functions
Equation Of The Ascent Path Of An Airplane
Calculating Capacity Of A Video Adapter Board Memory
Probability Density Functions
Boolean Algebra - Logic Functions
Ordinary Differential Equations (ODEs)
Infinite Sequences And Series
Introduction To Group Theory
Advanced Calculus - Partial Derivatives
Advanced Calculus - General Charateristics Of Partial Differential Equations
Advanced Calculus - Jacobians
Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables
Advanced Calculus - Fourier Series
Advanced Calculus - Multiple Integrals
Production Schedule That Maximizes Profit Given Constraint Equation
Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation
Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions
Derivation Of Heat Equation For A One-Dimensional Heat Flow
The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light.
Composition And Structure Of Matter
How Matter Gets Composed
How Matter Gets Composed (2)
Molecular Structure Of Matter
Molecular Shapes: Bond Length, Bond Angle
Molecular Shapes: Valence Shell Electron Pair Repulsion
Molecular Shapes: Orbital Hybridization
Molecular Shapes: Sigma Bonds Pi Bonds
Molecular Shapes: Non ABn Molecules
Molecular Orbital Theory
More Pj Problem Strings